Sun 26 Jan 2020 03:51:10 PM -03

Index

• Difference between meteorological and traffic-jam-style predictions: 18.
• Frequent assumption (but not always) on game theory that individuals knows the rules of the game; that they even known their inner motives: 28.
• Individualism, separation of structure and choice, 31.
• MAD, 86; 88.
• Elimination of non-credible threats, 88.

Excerpts

Intro

What is game theory:

In many respects this enthusiasm is not difficult to understand. Game theory
was probably born with the publication of The Theory of Games and Economic
Behaviour by John von Neumann and Oskar Morgenstern (first published in
1944 with second and third editions in 1947 and 1953). They defined a game
as any interaction between agents that is governed by a set of rules
specifying the possible moves for each participant and a set of outcomes for
each possible combination of moves.

How it can help:

If game theory does make a further substantial contribution, then we
believe that it is a negative one. The contribution comes through
demonstrating the limits of a particular form of individualism in social
science: one based exclusively on the model of persons as preference satisfiers.
This model is often regarded as the direct heir of David Hume’s (the 18th
century philosopher) conceptualisation of human reasoning and motivation. It
is principally associated with what is known today as rational choice theory, or
with the (neoclassical) economic approach to social life (see Downs, 1957, and
Becker, 1976). Our main conclusion on this theme (which we will develop
through the book) can be rephrased accordingly: we believe that game theory
reveals the limits of ‘rational choice’ and of the (neoclassical) economic
approach to life. In other words, game theory does not actually deliver Jon
Elster’s ‘solid microfoundations’ for all social science; and this tells us
something about the inadequacy of its chosen ‘microfoundations’.

Assumptions:

three key assumptions: agents are instrumentally
rational (section 1.2.1); they have common knowledge of this rationality
(section 1.2.2); and they know the rules of the game (section 1.2.3).
These assumptions set out where game theory stands on the big questions of
the sort ‘who am I, what am I doing here and how can I know about either?’.
The first and third are ontological. 1 They establish what game theory takes as
the material of social science: in particular, what it takes to be the essence of
individuals and their relation in society. The second raises epistemological
issues 2 (and in some games it is not essential for the analysis). It is concerned
with what can be inferred about the beliefs which people will hold about how
games will be played when they have common knowledge of their rationality.

Instrumental rationality (Homo economicus):

We spend more time discussing these assumptions than is perhaps usual in
texts on game theory because we believe that the assumptions are both
controversial and problematic, in their own terms, when cast as general
propositions concerning interactions between individuals. This is one respect
in which this is a critical introduction. The discussions of instrumental
rationality and common knowledge of instrumental rationality (sections 1.2.1
and 1.2.2), in particular, are indispensable for anyone interested in game
theory. In comparison section 1.2.3 will appeal more to those who are
concerned with where game theory fits in to the wider debates within social

[...]

Individuals who are instrumentally rational have preferences over various
‘things’, e.g. bread over toast, toast and honey over bread and butter, rock
over classical music, etc., and they are deemed rational because they select
actions which will best satisfy those preferences. One of the virtues of this
model is that very little needs to be assumed about a person’s preferences.
Rationality is cast in a means-end framework with the task of selecting the
most appropriate means for achieving certain ends (i.e. preference
satisfaction); and for this purpose, preferences (or ‘ends’) must be coherent
in only a weak sense that we must be able to talk about satisfying them more
or less. Technically we must have a ‘preference ordering’ because it is only
when preferences are ordered that we will be able to begin to make
judgements about how different actions satisfy our preferences in different
degrees.

[...]

Thus it appears a promisingly general model of action. For instance, it could
apply to any type of player of games and not just individuals. So long as the
State or the working class or the police have a consistent set of objectives/
preferences, then we could assume that it (or they) too act instrumentally so
as to achieve those ends. Likewise it does not matter what ends a person
pursues: they can be selfish, weird, altruistic or whatever; so long as they
consistently motivate then people can still act so as to satisfy them best.

An agent is "rational" in this conext when they have preference ordering" and if "they select the action that maximizes those preferences:

Readers familiar with neoclassical Homo economicus will need no further
introduction. This is the model found in standard introductory texts, where
preferences are represented by indifference curves (or utility functions) and
agents are assumed rational because they select the action which attains the
highest feasible indifference curve (maximises utility). For readers who have
not come across these standard texts or who have forgotten them, it is worth
explaining that preferences are sometimes represented mathematically by a
utility function. As a result, acting instrumentally to satisfy best one’s
preferences becomes the equivalent of utility maximising behaviour.

Reason and slavery:

Even when we accept the Kantian argument, it is plain that reason’s
guidance is liable to depend on characteristics of time and place. For
example, consider the objective of ‘owning another person’. This obviously
does not pass the test of the categorical imperative since all persons could
not all own a person. Does this mean then we should reject slave-holding? At
first glance, the answer seems to be obvious: of course, it does! But notice it
will only do this if slaves are considered people. Of course we consider
slaves people and this is in part why we abhor slavery, but ancient Greece
did not consider slaves as people and so ancient Greeks would not have been
disturbed in their practice of slavery by an application of the categorical
imperative.

Reason dependent on culture:

Wittgenstein suggests that if you want to know why people act in the way that
they do, then ultimately you are often forced in a somewhat circular fashion to
say that such actions are part of the practices of the society in which those
persons find themselves. In other words, it is the fact that people behave in a
particular way in society which supplies the reason for the individual person to
act: or, if you like, actions often supply their own reasons. This is shorthand
description rather than explanation of Wittgenstein’s argument, but it serves to
make the connection to an influential body of psychological theory which
makes a rather similar point.

Cognitive dissonance and free market proponents:

Festinger’s (1957) cognitive dissonance theory proposes a model where
reason works to ‘rationalise’ action rather than guide it. The point is that we
often seem to have no reason for acting the way that we do. For instance, we
may recognise one reason for acting in a particular way, but we can equally
recognise the pull of a reason for acting in a contrary fashion. Alternatively,
we may simply see no reason for acting one way rather than another. In such
circumstances, Festinger suggests that we experience psychological distress. It
comes from the dissonance between our self-image as individuals who are
authors of our own action and our manifest lack of reason for acting. It is like
a crisis of self-respect and we seek to remove it by creating reasons. In short
we often rationalise our actions ex post rather than reason ex ante to take them
as the instrumental model suggests.

[...]

Research has shown that people seek out and read advertisements for
the brand of car they have just bought. Indeed, to return us to economics, it is
precisely this insight which has been at the heart of one of the Austrian and
other critiques of the central planning system when it is argued that planning
can never substitute for the market because it presupposes information
regarding preferences which is in part created in markets when consumers
choose.

Infinite regress of the economics of information acquisiton (i.e learning, eg. from a secret service):

Actually most game theorists seem to agree on one aspect of the problem
of belief formation in the social world: how to update beliefs in the presence
of new information. They assume agents will use Bayes’s rule. This is explained
in Box 1.6. We note there some difficulties with transplanting a technique from
the natural sciences to the social world which are related to the observation we
have just made. We focus here on a slightly different problem. Bayes provides
a rule for updating, but where do the original (prior) expectations come from?
Or to put the question in a different way: in the absence of evidence, how do
agents form probability assessments governing events like the behaviour of
others?

There are two approaches in the economics literature. One responds by
suggesting that people do not just passively have expectations. They do not
just wait for information to fall from trees. Instead they make a conscious
decision over how much information to look for. Of course, one must have
started from somewhere, but this is less important than the fact that the
acquisition of information will have transformed these original ‘prejudices’.
The crucial question, on this account, then becomes: what determines the
amount of effort agents put into looking for information? This is deceptively
easy to answer in a manner consistent with instrumental rationality. The
instrumentally rational agent will keep on acquiring information to the point
where the last bit of search effort costs her or him in utility terms the same
amount as the amount of utility he or she expects to get from the
information gained by this last bit of effort. The reason is simple. As long as
a little bit more effort is likely to give the agent more utility than it costs,
then it will be adding to the sum of utilities which the agent is seeking to
maximise.

[...]

This looks promising and entirely consistent with the definition of
instrumentally rational behaviour. But it begs the question of how the agent
knows how to evaluate the potential utility gains from a bit more information
_prior to gaining that information_. Perhaps he or she has formulated expectations of
the value of a little bit more information and can act on that. But then the
problem has been elevated to a higher level rather than solved. How did he or
she acquire that expectation about the value of information? ‘By acquiring
information about the value of information up to the point where the
marginal benefits of this (second-order) information were equal to the costs’,
is the obvious answer. But the moment it is offered, we have the beginnings of
an infinite regress as we ask the same question of how the agent knows the
value of this second-order information. To prevent this infinite regress, we
must be guided by something _in addition_ to instrumental calculation. But this
means that the paradigm of instrumentally rational choices is incomplete. The
only alternative would be to assume that the individual _knows_ the benefits that
he or she can expect on average from a little more search (i.e. the expected
marginal benefits) because he or she knows the full information set. But then
there is no problem of how much information to acquire because the person
knows everything!

Infinite recursion of the common knowledge (CKR):

If you want to form an expectation about what somebody does, what
could be more natural than to model what determines their behaviour and
then use the model to predict what they will do in the circumstances that
interest you? You could assume the person is an idiot or a robot or whatever,
but most of the time you will be playing games with people who are
instrumentally rational like yourself and so it will make sense to model your
opponent as instrumentally rational. This is the idea that is built into the
analysis of games to cover how players form expectations. We assume that
there is common knowledge of rationality held by the players. It is at once
both a simple and complex approach to the problem of expectation
formation. The complication arises because with common knowledge of
rationality I know that you are instrumentally rational and since you are
rational and know that I am rational you will also know that I know that you
are rational and since I know that you are rational and that you know that I
am rational I will also know that you know that I know that you are rational
and so on…. This is what common knowledge of rationality means.

[...]

It is difficult to pin down because common knowledge of X
(whatever X may be) cannot be converted into a finite phrase beginning with ‘I
know…’. The best one can do is to say that if Jack and Jill have common
knowledge of X then ‘Jack knows that Jill knows that Jack knows …that Jill
knows that Jack knows…X’—an infinite sentence. The idea reminds one of
what happens when a camera is pointing to a television screen that conveys the
image recorded by the very same camera: an infinite self-reflection. Put in this
way, what looked a promising assumption suddenly actually seems capable of
leading you anywhere.

[...]

The problem of expectation formation spins hopelessly out of control.

Nevertheless game theorists typically assume CKR and many of them, and
certainly most people who apply game theory in economics and other
disciplines

Uniformity: Consistent Alignment of Beliefs (CAB), another weak assumption based on Harsanyi doctrine requiring equal information; followed by a comparison with Socract dialectics:

Put informally, the notion of _consistent alignment of beliefs_ (CAB) means that
no instrumentally rational person can expect another similarly rational
person who has the same infor mation to develop different thought
processes. Or, alternatively, that no rational person expects to be surprised
by another rational person. The point is that if the other person’s thought is
genuinely moving along rational lines, then since you know the person is
rational and you are also rational then your thoughts about what your
rational opponent might be doing will take you on the same lines as his or
her own thoughts. The same thing applies to others provided they respect
_your_ thoughts. So your beliefs about what your opponents will do are
consistently aligned in the sense that if you actually knew their plans, you
would not want to change your beliefs; and if they knew your plans they
would not want to change the beliefs they hold about you and which support
their own planned actions.

Note that this does not mean that everything can be deterministically
predicted.

Reason reflecting on itself:

These observations are only designed to signal possible trouble ahead
and we shall examine this issue in greater detail in Chapters 2 and 3. We
conclude the discussion now with a pointer to wider philosophical currents.
Many decades before the appearance of game theor y, the Ger man
philosophers G.F.W.Hegel and Immanuel Kant had already considered the
notion of the self-conscious reflection of human reasoning on itself. Their
main question was: can our reasoning faculty turn on itself and, if it can,
what can it infer? Reason can certainly help persons develop ways of
cultivating the land and, therefore, escape the tyranny of hunger. But can it
understand how it, itself, works? In game theory we are not exactly
concerned with this issue but the question of what follows from common
knowledge of rationality has a similar sort of reflexive structure. When
reason knowingly encounters itself in a game, does this tell us anything
about what reason should expect of itself?

What is revealing about the comparison between game theory and
thinkers like Kant and Hegel is that, unlike them, game theory offers
something settled in the form of CAB. What is a source of delight,
puzzlement and uncertainty for the German philosophers is treated as a
problem solved by game theory. For instance, Hegel sees reason reflecting
on reason as it reflects on itself as part of the restlessness which drives
human history. This means that for him there are no answers to the
question of what reason demands of reason in other people outside of
human history. Instead history offers a changing set of answers. Likewise
Kant supplies a weak answer to the question. Rather than giving substantial
advice, reason supplies a negative constraint which any principle of
knowledge must satisfy if it is to be shared by a community of rational
people: any rational principle of thought must be capable of being followed
by all. O’Neill (1989) puts the point in the following way:

    [Kant] denies not only that we have access to transcendent meta-
    physical truths, such as the claims of rational theology, but also that
    reason has intrinsic or transcendent vindication, or is given in
    consciousness. He does not deify reason. The only route by which we
    can vindicate certain ways of thinking and acting, and claim that those
    ways have authority, is by considering how we must discipline our
    thinking if we are to think or act at all. This disciplining leads us not to
    algorithms of reason, but to certain constraints on all thinking,
    communication and interaction among any plurality. In particular we are
    led to the principle of rejecting thought, act or communication that is
    guided by principles that others cannot adopt.
    (O’Neill p. 27)

Summary:

To summarise, game theory is avowedly Humean in orientation.  [...]
The second [aspect] is that game theorists seem to assume _too much_ on behalf
of reason [even more than Hume did].

Giddens, Wittgenstein language games and the "organic or holistic view of the relation between action and structure" (pages 30-31):

The question is ontological and it connects directly with the earlier
discussion of instrumental rationality. Just as instrumental rationality is not
the only ontological view of what is the essence of human rationality, there is
more than one ontological view regarding the essence of social interaction.
Game theory works with one view of social interaction, which meshes well
with the instrumental account of human rationality; but equally there are
other views (inspired by Kant, Hegel, Marx, Wittgenstein) which in turn
require different models of (rational) action.

State (pages 32-33):

Perhaps the most famous example of this type of
institutional creation comes from the early English philosopher Thomas
Hobbes who suggested in Leviathan that, out of fear of each other,
individuals would contract with each other to form a State. In short, they
would accept the absolute power of a sovereign because the sovereign’s
ability to enforce contracts enables each individual to transcend the dog-
eat-dog world of the state of nature, where no one could trust anyone and
life was ‘short, nasty and brutish’.

Thus, the key individualist move is to draw attention to the way that
structures not only constrain; they also enable (at least those who are in a
position to create them). It is the fact that they enable which persuades
individuals consciously (as in State formation) or unconsciously (in the case
of those which are generated spontaneously) to build them. To bring out
this point and see how it connects with the earlier discussion of the
relation between action and structure it may be helpful to contrast Hobbes
with Rousseau. Hobbes has the State emerging from a contract between
individuals because it serves the interests of those individuals. Rousseau
also talked of a social contract between individuals, but he did not speak
this individualist language. For him, the political (democratic) process was
not a mere means of ser ving persons’ interests by satisfying their
preferences. It was also a process which changed people’s preferences. People
were socialised, if you like, and democracy helped to create a new human
being, more tolerant, less selfish, better educated and capable of cherishing
the new values of the era of Enlightenment. By contrast, Hobbes’ men and
women were the same people before and after the contract which created
the State. 4

Game theory as justification of individualism (pages 32-33), which reminds the discussion made by Dany-Robert Dufour in La Cite Perverse; it is also noted that the State is considered a "collective action agency":

Where do structures come from when they are separate from actions?  An
ambitious response which distinguishes methodological individualists of all
types is that the structures are merely the deposits of previous interactions
(potentially understood, of course, as games). This answer may seem to threaten
an infinite regress in the sense that the structures of the previous
interaction must also be explained and so on. But, the individualist will want
to claim that ultimately all social str uctures spring from interactions
between some set of asocial individuals; this is why it is ‘individualist’.

[...]

Returning to game theory’s potential contribution, we can see that, in so
far as individuals are modelled as Humean agents, game theory is well placed
to help assess the claims of methodological individualists. After all, game
theory purports to analyse social interaction between individuals who, as
Hume argued, have passions and a reason to serve them. Thus game theory
should enable us to examine the claim that, beginning from a situation with
no institutions (or structures), the self-interested behaviour of these
instrumentally rational agents will either bring about institutions or fuel their
evolution. An examination of the explanatory power of game theory in such
settings is one way of testing the individualist claims.
In fact, as we shall see in subsequent chapters, the recurring difficulty

[...]

Suppose we take the methodological individualist route and see
institutions as the deposits of previous interactions between individuals.
Individualists are not bound to find that the institutions which emerge in
this way are fair or just. Indeed, in practice, many institutions reflect the
fact that they were created by one group of people and then imposed on
other groups. All that any methodological individualist is committed to is
being able to find the origin of institutions in the acts of individuals qua
individuals. The political theory of liberal individualism goes a stage
further and tries to pass judgement on the legitimacy of particular
institutions. Institutions in this view are to be regarded as legitimate in so
far as all individuals who are governed by them would have broadly
‘agreed’ to their creation.

Naturally, much will turn on how ‘agreement’ is to be judged because
people in desperate situations will often ‘agree’ to the most desperate of
outcomes. Thus there are disputes over what constitutes the appropriate
reference point (the equivalent to Hobbes’s state of nature) for judging
whether people would have agreed to such and such an arrangement. We set
aside a host of further problems which emerge the moment one steps outside
liberal individualist premises and casts doubt over whether people’s
preferences have been autonomously chosen. Game theory has little to
contribute to this aspect of the dispute. However, it does make two
significant contributions to the discussions in liberal individualism with
respect to how we might judge ‘agreement’.

Prisioner's dilemma and the hobbesian argument for the creation of a State (pages 36-37): resolution would require a higher State in the next upper level of recursion:

Finally there is the prisoners’ dilemma game (to which we have dedicated the
whole of Chapter 5 and much of Chapter 6). Recall the time when there were
still two superpowers each of which would like to dominate the other, if
possible. They each faced a choice between arming and disarming. When both
arm or both disarm, neither is able to dominate the other. Since arming is
costly, when both decide to arm this is plainly worse than when both decide to
disarm. However, since we have assumed each would like to dominate the
other, it is possible that the best outcome for each party is when that party
arms and the other disarms since although this is costly it allows the arming
side to dominate the other. These preferences are reflected in the ‘arbitrary’
utility pay-offs depicted in Figure 1.4.

Game theory makes a rather stark prediction in this game: both players will
arm (the reasons will be given later). It is a paradoxical result because each
does what is in their own interest and yet their actions are collectively self-
defeating in the sense that mutual armament is plainly worse than the
alternative of mutual disarmament which was available to them (pay-off 1 for
utility pay-offs depicted in Figure 1.4.

Game theory makes a rather stark prediction in this game: both players will
arm (the reasons will be given later). It is a paradoxical result because each
does what is in their own interest and yet their actions are collectively self-
defeating in the sense that mutual armament is plainly worse than the
alternative of mutual disarmament which was available to them (pay-off 1 for
each rather than 2). The existence of this type of interaction together with the
inference that both will arm has provided one of the strongest arguments for
the creation of a State. This is, in effect, Thomas Hobbes’s argument in
Leviathan. And since our players here are themselves States, both countries
should agree to submit to the authority of a higher State which will enforce an
agreement to disar m (an argument for a strong, independent, United
Nations?).

Too much trust in that type of instrumental rationality might lead to lower outcomes in some games:

The term rationalisable has been used to describe such strategies because a
player can defend his or her choice (i.e. rationalise it) on the basis of beliefs
about the beliefs of the opponent which are not inconsistent with the game’s
data. However, to pull this off, we need ‘more’ commonly known rationality
than in the simpler games in Figures 2.1 and 2.3. Looking at Figure 2.4 we see
that outcome (100, 90) is much more inviting than the rationalisable outcome
(1, 1). It is the deepening confidence in each other’s instrumental rationality
(fifth-order CKR, to be precise) which leads our players to (1, 1). In summary
notation, the rationalisable strategies R2, C2 are supported by the following
train of thinking (which reflects the six steps described earlier):

-- 48

Nash-equilibrium: self-confirming strategy:

A set of rationalisable strategies (one for each player) are in a Nash
equilibrium if their implementation confirms the expectations of each player
about the other’s choice.  Put differently, Nash strategies are the only
rationalisable ones which, if implemented, confirm the expectations on which
they were based. This is why they are often referred to as self-confirming
strategies or why it can be said that this equilibrium concept requires that
players’ beliefs are consistently aligned (CAB).

-- 53

Arguments against CAB:

In the same spirit, it is sometimes argued (borrowing a line from John von
Neumann and Oskar Morgenstern) that the objective of any analysis of games is
the equivalent of writing a book on how to play games; and the minimum
condition which any piece of advice on how to play a game must satisfy is
simple: the advice must remain good advice once the book has been published.
In other words, it could not really be good advice if people would not want to
follow it once the advice was widely known. On this test, only (R2, C2) pass,
since when the R player follows the book’s advice, the C player would want to
follow it as well, and vice versa. The same cannot be said of the other
rationalisable strategies. For instance, suppose (R1, C1) was recommended: then
R would not want to follow the advice when C is expected to follow it by
selecting C1 and likewise, if R was expected to follow the advice, C would not
want to.

Both versions of the argument with respect to what mutual rationality entails
seem plausible. Yet, there is something odd here. Does respect for each other’s
rationality lead each person to believe that neither will make a mistake in a
game? Anyone who has talked to good chess players (perhaps the masters of
strategic thinking) will testify that rational persons pitted against equally
rational opponents (whose rationality they respect) do not immediately assume
that their opposition will never make errors. On the contrary, the point in
chess is to engender such errors! Are chess players irrational then?  One is
inclined to answer no, but why? And what is the difference as

-- 57

Limits conceptualizing reason as an algorithm ("Humean approach to reason is algorithmic"):

Harsanyi doctrine seems to depend on a powerfully algorithmic and controversial
view of reason. Reason on this account (at least in an important part) is akin
to a set of rules of inference which can be used in moving from evidence to
expectations. That is why people using reason (because they are using the same
algorithms) should come to the same conclusion. However, there is genuine
puzzlement over whether such an algorithmic view of reason can apply to all
circumstances. Can any finite set of rules contain rules for their own
application to all possible circumstances? The answer seems to be no, since
under some sufficiently detailed level of description there will be a question of
whether the rule applies to this event and so we shall need rules for applying
the rules for applying the rules. And as there is no limit to the detail of the
description of events, we shall need rules for applying the rules for applying
the rules, and so on to infinity. In other words, every set of rules will require
creative interpretation in some circumstances and so in these cases it is
perfectly possible for two individuals who share the same rules to hold
divergent expectations.

This puts a familiar observation from John Maynard Keynes and Frank
Knight regarding genuine uncertainty in a slightly different way, but
nevertheless it yields the same conclusion. There will be circumstances under
which individuals are unable to decide rationally what probability assessment
to attach to events because the events are uncertain and so it should not be
surprising to find that they disagree. Likewise, the admiration for
entrepreneurship found among economists of the Austrian school depends on
the existence of uncertainty. Entrepreneurship is highly valued precisely
because, as a result of uncertainty, people can hold different expectations
regarding the future. In this context, the entrepreneurs are those who back
their judgement against that of others and succeed. In other words, there
would be no job for entrepreneurs if we all held common expectations in a
world ruled by CAB!

A similar conclusion regarding ineliminable uncertainty is shared by social
theorists who have been influenced by the philosophy of Kant. They deny that
reason should be understood algorithmically or that it always supplies answers
as to what to do. For Kantians reason supplies a critique of itself which is the
source of negative restraints on what we can believe rather than positive
instructions as to what we should believe. Thus the categorical imperative (see
section 1.2.1), which according to Kant ought to determine many of our
significant choices, is a sieve for beliefs and it rarely singles out one belief.
Instead, there are often many which pass the test and so there is plenty of
room for disagreement over what beliefs to hold.

Perhaps somewhat surprisingly though, a part of Kant’s argument might
lend support to the Nash equilibrium concept. In particular Kant thought that
rational agents should only hold beliefs which are capable of being
universalised. This idea, taken by itself, might prove a powerful ally of Nash.
[...] Of course, a full Kantian perspective is
likely to demand rather more than this and it is not typically adopted by game
theorists. Indeed such a defence of Nash would undo much of the
foundations of game theory: for the categorical imperative would even
recommend choosing dominated strategies if this is the type of behaviour that
each wished everyone adopted. Such thoughts sit uncomfortably with the
Humean foundations of game theory and we will not dwell on them for now.
Instead, since the spirit of the Humean approach to reason is algorithmic, we
shall continue discussing the difficulties with the Harsanyi—Aumann defence
of Nash.

-- 58-60

"Irrational" plays which might intend to send a message to other players:

Indeed why should one assume in this way that players cannot (or
should not) try to make statements about themselves through patterning
their ‘trembles? The question becomes particularly sharp once it is recalled
that, on the conventional account, players must expect that there is always
some chance of a tremble. Trembles in this sense are part of normal
behaviour, and the critics argue that agents may well attempt to use them
as a medium for signalling something to each other. Of course, players will
not do so if they believe that their chosen pattern is going to be ignored
by others. But that is the point: why assume that this is what they will
believe from the beginning, especially when agents can see that the
generally accepted use of trembles as signals might secure a better
outcome for both players [...]?

Note that this is not an argument against backward induction per se: it is an
argument against assuming CKR while working out beliefs via backward
induction (i.e. a criticism of Nash backward induction). When agents consider
patterning their ‘trembles’, they project forward about future behaviour given
that there are trembles now or in the past. What makes it ambiguous whether
they should do this, or stick to Nash backward induction instead, is that there
is no uniquely rational way of playing games like Figures 3.5 or 3.6 (unlike the
race to 20 game in which there is). In this light, the subgame perfect Nash
equilibrium offers one of many possible scenarios of how rational agents will
behave.

-- 93

Why not expand this affirmation so any move to signal some intention?

Misc

Page 101:

Hence these refinements (e.g. proper equilibria), likethe Nash
equilibrium project itself, seem to have to appeal to somethingother
than the traditional assumptions of game theory regarding
rationalaction in a social context.

Page 102:

regarding the relation betweenconvention following and instrumental
rationality. The worry here takes usback to the discussion of section
1.2.3 where for instance it was suggested thatconventions might best be
understood in the way suggested by Wittgenstein orHegel. In short, the
acceptance of convention may actually require a radicalreassessment of
the ontological foundations of game theory.

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actually require a radicalreassessment of the ontological foundations
of game theory.

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Why not give up on the Nash concept altogether? This ‘giving up’ might
takeon one of two forms. Firstly, game theory could appeal to the
concept ofrationalisable strategies (recall section 2.4 of Chapter 2)
which seemuncontentiously to flow from the assumptions of instrumental
rationalityand CKR. The difficulty with such a move is that it concedes
that gametheory is unable to say much about many games (e.g. Figures
2.6, 2.12, etc.).Naturally, modesty of this sort might be entirely
appropriate for gametheory, although it will diminish its claims as a
solid foundation for socialscience.

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Unlike the instrumentally rational model, for Hegelians and Marxists
actionbased on preferences feeds back to affect preferences, and so on,
in an everunfolding chain. (See Box 3.1 for a rather feeble attempt to
blend desires andbeliefs.) Likewise some social psychologists might
argue that the key to actionlies less with preferences and more with
the cognitive processes used bypeople; and consequently we should
address ourselves to understanding theseprocesses.

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105

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Quite simply, the significant social processes which write history
cannot beunderstood through the lens of instrumental rationality. This
destines gametheory to a footnote in some future text on the history of
social theory. Welet the reader decide.3

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Thirdly, the sociology of the discipline may provide further clues.
Twoconditions would seem to be essential for the modern development of
adiscipline within the academy. Firstly the discipline must be
intellectuallydistinguishable from other disciplines. Secondly, there
must be some barriersto the amateur pursuit of the discipline. (A third
condition which goes withoutsaying is that the discipline must be able
to claim that what it does ispotentially worth while.) The first
condition reduces the competition fromwithin the academy which might
come from other disciplines (to do thisworthwhile thing) and the second
ensures that there is no effectivecompetition from outside the academy.
In this context, the rational choicemodel has served economics very
well. It is the distinguishing intellectualfeature of economics as a
discipline and it is amenable to such formalisationthat it keeps most
amateurs well at bay. Thus it is plausible to argue that thesuccess of
economics as a discipline within the social sciences has been
closelyrelated to its championing of the rational choice model.

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kind of amnesia or lobotomy which thediscipline seems to have suffered
regarding most things philosophical duringthe postwar period.

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It isoften more plausible to think of the academy as a battleground
betweendisciplines rather than between ideas and the disciplines which
have goodsurvival features (like the barriers to entry identified
above)

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explanations willonly prosper in so far as they are both superior and
they are not institutionallyundermined by the rise of neoclassical
economics and the demise ofsociology. It is not necessary to see these
things conspiratorially to see thepoint of this argument. All academics
have fought their corner in battles overresources and they always use
the special qualities of their discipline asammunition in one way or
another. Thus one might explain in functionalist termsthe mystifying
attachment of economics and game theory to Nash.

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We have no special reason to prioritise one strand of our
proposedexplanation. Yet, there is more than a hint of irony in the
last suggestionbecause Jon Elster has often championed game theory and
its use of the Nashequilibrium concept as an alternative to functional
arguments in social science.Well, if the use of Nash by game theorists
is itself to be explainedfunctionally, then…

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Liberal theorists often explain the State with reference to state of
nature. Forinstance, within the Hobbesian tradition there is a stark
choice between astate of nature in which a war of all against all
prevails and a peacefulsociety where the peace is enforced by a State
which acts in the interest ofall. The legitimacy of the State derives
from the fact that people who wouldotherwise live in Hobbes’s state of
nature (in which life is ‘brutish, nasty andshort’) can clearly see the
advantages of creating a State. Even if a State had

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not surfaced historically for all sorts of other reasons, it would have
to beinvented.Such a hypothesised ‘invention’ would require a
cooperative act of comingtogether to create a State whose purpose will
be to secure rights over life andproperty. Nevertheless, even if all
this were common knowledge, it wouldnot guarantee that the State will
be created. There is a tricky further issuewhich must be resolved. The
people must agree to the precise property rightswhich the State will
defend and this is tricky because there are typically avariety of
possible property rights and the manner in which the benefits ofpeace
will be distributed depends on the precise property rights which
areselected (see Box 4.1).In other words, the common interest in peace
cannot be the onlyelement in the liberal explanation of the State, as
any well-defined andpoliced property rights will secure the peace. The
missing element is anaccount of how a particular set of property rights
are selected and thiswould seem to require an analysis of how people
resolve conflicts ofinterest. This is where bargaining theory promises
to make an importantcontribution to the liberal theory of the State
because it is concernedprecisely with interactions of this sort.

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State creation in Hobbes’s world provides one example (which
especiallyinterests us because it suggests that bargaining theory may
throw light onsome of the claims of liberal political theory with
respect to the State), butthere are many others.

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The creation of the institutions for enforcing agreements (like the
State)which are presumed by cooperative game theory requires as we have
seenthat agents first solve the bargaining problem non-cooperatively.

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Indeed for this reason, and following thepractice of most game
theorists, we have so far discussed the non-cooperative play of games
‘as if ’ there was no communication, therebyimplicitly treating any
communication which does take place in the absenceof an enforcement
agency as so much ‘cheap talk’

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In cooperative games agents cantalk to each other and make agreements
which are binding on later play. Innon-cooperative games, no agreements
are binding. Players can say whateverthey like, but there is no
external agency which will enforce that they dowhat they have said they
will do.

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Thus it will have shown not just what sort of State rational agents
mightagree to create, but also how rational agents might solve a host
of bargainingproblems in social life. Unfortunately we have reasons to
doubt therobustness of this analysis and it is not difficult to see our
grounds forscepticism. If bargaining games resemble the hawk-dove game
and thediscussion in Chapter 2 is right to point to the existence of
multipleequilibria in this game under the standard assumptions of game
theory, thenhow does bargaining theory suddenly manage to generate a
uniqueequilibrium?

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114face value, the striking result of the non-cooperative analysis of
thebargaining problem is that it yields the same solution to the
bargainingproblem as the axiomatic approach. If this result is robust,
then it seems thatgame theory will have done an extraordinary service
by showing thatbargaining problems have unique solutions (whichever
route is preferred).Thus it will have shown not just what sort of State
rational agents mightagree to create, but also how rational agents
might solve a host of bargainingproblems in social life. Unfortunately
we have reasons to doubt therobustness of this analysis and it is not
difficult to see our grounds forscepticism. If bargaining games
resemble the hawk-dove game and thediscussion in Chapter 2 is right to
point to the existence of multipleequilibria in this game under the
standard assumptions of game theory, thenhow does bargaining theory
suddenly manage to generate a uniqueequilibrium?

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A threat or promise which, if carried out, costs more tothe agent who
issued it than if it is not carried out, iscalled an incredible threat
or promise.

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However, this failure topredict should be welcomed by John Rawls and
Robert Nozick as it providesan opening to their contrasting views of
what counts as justice betweenrational agents.

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If the Nash solution were unique, then game theory would have
answeredan important question at the heart of liberal theory over the
type of Statewhich rational agents might agree to create. In addition,
it would have solveda question in moral philosophy over what justice
might demand in this and avariety of social interactions. After all,
how to divide the benefits from socialcooperation seems at first sight
to involve a tricky question in moralphilosophy concerning what is
just, but if rational agents will only ever agreeon the Nash division
then there is only one outcome for rational agents.Whether we want to
think of this as just seems optional. But if we do or ifwe think that
justice is involved, then we will know, and for onceunambiguously, what
justice apparently demands between instrumentallyrational
agents.Unfortunately, though, it seems we cannot draw these inferences
becausethe Nash solution is not the unique outcome. Accepting this
conclusion, weare concerned in this section with what bargaining theory
then contributes tothe liberal project of examining the State as if it
were the result of rational

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behind the veil of ignorance.

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Torture: Another example in moral philosophy is revealed by the problem
oftorture for utilitarians. For instance, a utilitarian calculation
focuses onoutcomes by summing the individual utilities found in
society. In so doing itdoes not enquire about the fairness or otherwise
of the processes responsiblefor generating those utilities with the
result that it could sanction torture whenthe utility gain of the
torturer exceeds the loss of the person being tortured.Yet most people
would feel uncomfortable with a society which sanctionedtorture on
these grounds because it unfairly transgresses the ‘rights’ of
thetortured.

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Granted that society (andthe State) are not the result of some
living-room negotiation, what kind of“axioms” would have generated the
social outcomes which we observe in agiven society?’ That is, even if
we reject the preceding fictions (i.e. of the Stateas a massive
resolution of an n-person bargaining game, or of the veil ofignorance)
as theoretically and politically misleading, we may still
pinpointcertain axioms which would have generated the observed income
distributions(or distributions of opportunities, social roles, property
rights, etc.) as a resultof an (utterly) hypothetical bargaining game.

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Roemer (1988) considers a problem faced by an international
agencycharged with distributing some resources with the aim of
improving health(say lowering infant mortality rates). How should the
authority distributethose resources? This is a particularly tricky
issue because different countriesin the world doubtless subscribe to
some very different principles which theywould regard as relevant to
this problem; and so agreement on a particularrule seems unlikely.
Nevertheless, he suggests that we approach the problemby considering
the following constraints (axioms) which we might want toapply to the
decision rule because they might be the object of significantagreement.

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rule which allocates resources in such a way as to raise the country
with thelowest infant survival rate to that of the second lowest, and
then if the budgethas not been exhausted, it allocates resources to
these two countries until theyreach the survival rate of the third
lowest country, and so on until the budgetis exhausted.

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It is tempting to think that the problem only arises here because
theprisoners cannot communicate with one another. If they could get
togetherthey would quickly see that the best for both comes from ‘not
confessing’.But as we saw in the previous chapter, communication is not
all that isneeded. Each still faces the choice of whether to hold to an
agreement that

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The recognition ofthis predicament helps explain why individuals might
rationally submit to theauthority of a State, which can enforce an
agreement for ‘peace’. Theyvoluntarily relinquish some of their freedom
that they enjoy in the(hypothesised) state of nature to the State
because it unlocks the prisoners’dilemma. (It should be added perhaps
that this is not to be taken as a literalaccount of how all States or
enforcement agencies arise. The point of theargument is to demonstrate
the conditions under which a State or enforcementagency would enjoy
legitimacy among a population even though it restrictedindividual
freedoms.)

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their normal business with the result that they prosper and enjoy a
more‘commodious’ living (as Hobbes phrased it), choosing strategy
‘peace’ is like‘not confessing’ above; when everyone behaves in this
manner it is much betterthan when they all choose ‘war’ (’confess’).
However, and in spite of wideranging recognition that peace is better
than war, the same prisoners’ dilemmaproblem surfaces and leads to war.

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While Hobbes thought that the authority of the State should be absolute
soas to discourage any cheating on ‘peace’, he also thought the scope
of itsinterventions in this regard would be quite minimal. In contrast
much of themodern fascination with the prisoners’ dilemma stems from
the fact that theprisoners’ dilemma seems to be a ubiquitous feature of
social life. Forinstance, it plausibly lies at the heart of many
problems which groups

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they have struck over ‘not confessing’. Is it in the interest of either
party tokeep to such an agreement? No, a quick inspection reveals that
the bestaction in terms of pay-offs is still to ‘confess’. As Thomas
Hobbes remarkedin Leviathan when studying a similar problem, ‘covenants
struck without thesword are but words’. The prisoners may trumpet the
virtue of ‘notconfessing’ but if they are only motivated instrumentally
by the pay-offs,then it is only so much hot air because each will
‘confess’ when the timecomes for a decision.

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What seems to be required to avoid this outcome is a mechanism
whichallows for joint or collective decision making, thus ensuring that
both actuallydo ‘not confess’. In other words, there is a need for a
mechanism for enforcingan agreement—Hobbes’s ‘sword’, if you like. And
it is this recognition whichlies at the heart of a traditional liberal
argument dating back to Hobbes for thecreation of the State which is
seen as the ultimate enforcement agency.(Notice, however, that such an
argument applies equally to some otherinstitutions which have the
capacity to enforce agreements, for example theMafia.) In Hobbes’s
story, each individual in the state of nature can behavepeacefully or
in a war-like fashion. Since peace allows everyone to go about

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it is notuncommon to find the dilemma treated as the essential model of
social life

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The following four sectionsand the next chapter, on repeated games,
discuss some of the developmentsin the social science literature which
have been concerned with how thedilemma might be unlocked without the
services of the State. In otherwords, the later sections focus on the
question of whether the widespreadnature of this type of interaction
necessarily points to the (legitimate inliberal terms) creation of an
activist State. Are there other solutions whichcan be implemented
without involving the State or any public institution?Since the scope
of the State’s activities has become one of the mostcontested issues in
contemporary politics, it will come as no surprise todiscover that the
discussions around alternative solutions to the dilemmahave assumed a
central importance in recent political (and especially inliberal and
neoliberal) theory.

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It arises as a problem of trust in every elemental economic
exchangebecause it is rare for the delivery of a good to be perfectly
synchronised withthe payment for it and this affords the opportunity to
cheat on the

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These are two-person examples of the dilemma, but it is probably the
‘n-person’ version of the dilemma (usually called the free rider
problem) which hasattracted most attention. It creates a collective
action problem among groupsof individuals. Again the examples are
legion.

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The instrumentally rational individual will recognise that the best
action is‘do not attach’ (i.e. defection) whatever the others do. This
means that in apopulation of like-minded individuals, all will decide
similarly with the resultthat each individual gains 2 utils. This is
plainly an inferior outcome for allbecause everyone could have attached
the device and if they all had done soeach would have enjoyed 3
utils.In these circumstances the individuals in this economy might
agree to theState enforcing attachment of the device. Alternatively, it
is easy to see howanother popular intervention by the State would also
do the trick. The Statecould tax each individual who did not attach the
device a sum equivalent to 2utils and this would turn ‘attach’ (C) into
the dominant strategy.

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There is nothinglike the State which can enforce contracts within the
household to keep akitchen clean, but interestingly within a family
household one oftenobserves the exercise of patriarchal or paternal
power instead. Of course,the potential difficulty with such an
arrangement is that the patriarch mayrule in a partial manner with the
result that the kitchen is clean but with nohelp from the hands of the
patriarch! The role of the State has in suchcases been captured, so to
speak, by an interested party determined bygender. Then gender becomes
the determinant of who bears the burdenand who has the more privileged
role. Social power which ‘solves’prisoners’ dilemmas can be thus
exercised without the direct involvementof the State (even though the
State often enshrines such power in its owninstitutions).

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Hence the prisoners’ dilemma/free rider might plausibly lie atthe
distinction which is widely attributed to Marx in the discussion of
classconsciousness between a class ‘of itself’ and ‘for itself’ (see
Elster, 1986b). Onsuch a view a class transforms itself into a ‘class
for itself’, or a society avoidsdeficient demand, by unlocking the
dilemma.

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Adam Smith’s account of how the self-interest of sellers combines with
thepresence of many sellers to frustrate their designs and to keep
prices lowmight also fit this model of interaction. If you are the
seller choosing from thetwo row strategies C and D, then imagine that C
and D translate into ‘charge ahigh price’ and ‘charge a low price’
respectively. Figure 5.2 could reflect yourpreference ordering as high
prices for all might be better than low prices forall and charging a
low price when all others charge a high might be the bestoption because
you scoop market share. Presumably the same applies to yourcompetitors.
Thus even though all sellers would be happier with a high level
ofprices, their joint interest is subverted because each acting
individually quiterationally charges a low price. It is as if an
invisible hand was at work onbehalf of the consumers.

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This is perhaps the most radical departure from the
conventionalinstrumental understanding of what is entailed by
rationality because, whileaccepting the pay-offs, it suggests that
agents should act in a different wayupon them. The notion of
rationality is no longer understood in the means—end framework as the
selection of the means most likely to satisfy given ends.

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thus enabling‘rationality’ to solve the problem when there are
sufficient numbers ofKantian agents.

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For instance, we mighthave wrongly assumed earlier that there is no
honour among thieves becauseacting honourably could be connected to
acting rationally in some fullaccount of rationality in which case the
dilemma might be unlocked withoutthe intervention of the State (or some
such agency). This general idea oflinking a richer notion of rational
agency with the spontaneous solution ofthe dilemma has been variously
pursued in the social science literature andthis section and the
following three consider four of the more prominentsuggestions.

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The first connects rationality with morality and Kant provides a
readyreference. His practical reason demands that we should undertake
thoseactions which when generalised yield the best outcomes. It does
not matterwhether others perform the same calculation and actually
undertake thesame action as you. The morality is deontological and it
is rational for theagent to be guided by a categorical imperative (see
Chapter 1). Consequently,in the free rider problem, the application of
the categorical imperative willinstruct Kantian agents to follow the
cooperative action

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Similarly partisans in occupied Europe during the Second World War
riskedtheir lives even when it was not clear that it was instrumentally
rational toconfront the Nazis. In such cases, it seems people act on a
sense of what isright.

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Likewise, Hardin (1982) suggests thatthe existence of environmental and
other voluntary organisations usuallyentails overcoming a free rider
problem and in the USA this may beexplained in part by an American
commitment to a form ofcontractarianism whereby ‘people play fair if
enough others do’

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Instead, rationality is conceived more as an expression of what is
possible: ithas become an end in its own right. This is not only
radical, it is alsocontroversial. Deontological moral philosophy is
controversial for the obviousreason that it is not concerned with the
actual consequences of an action, aswell as for the move to connect it
with rationality. (Nevertheless, O’Neill(1989) presents a recent
argument and provides an extended discussion of thismoral psychology
and how it might be applied.)Kant’s morality may seem rather demanding
for these reasons, but thereare weaker or vaguer types of moral
motivation which also seem capableof unlocking the prisoners’ dilemma.
For example, a general altruisticconcern for the welfare of others may
provide a sufficient reason forpeople not to defect on the cooperative
arrangement.

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Another departure from the strict instrumental model of rational action
comeswhen individuals make decisions in a context of norms and these
norms arecapable of overriding considerations of what is instrumentally
rational.

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On the other hand, given the well-known difficultiesassociated with any
coherent system of ethics (like utilitarianism), it seemsquite likely
that a person’s ethical concerns will not be captured by a well-behaved
set of preferences (see for instance Sen (1970) on the problems ofbeing
a Paretian Liberal). Indeed rational agents may well base their actions
onreasons which are external to their preferences.

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Of course, there is a tricky issue concerning whether these rather
weaker orvaguer moral motivations (like altruism, acting on what is
fair or what is right)mark a deep breach with the instrumental model of
action. It might be arguedthat such ethical concerns can be represented
in this model by introducing theconcept of ethical preferences. Thus
the influence of ethical preferencestransforms the pay-offs in the
game.

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Disputeswithin Aboriginal society are neither perceived as simply
between twoindividuals nor subject to some established community
tribunal. It is for thisreason that the resolution of a major conflict
will involve a significant amountof negotiation between the parties.
Yet the informal laws which govern thecontents of the negotiations are
well entrenched in the tribal culture. Forexample, it is not uncommon
for family members of the perpetrator to beasked to accept ‘punishment’
if the individual offender is in prison andtherefore unavailable.

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First World War. This was a war of unprecedentedcarnage both at the
beginning and the end. Yet during a middle period, non-aggression
between the two opposing trenches emerged spontaneously in theform of a
‘live and let live’ norm. Christmas fraternisation is one
well-knownexample, but the ‘live and let live’ norm was applied much
more widely.Snipers would not shoot during meal times and so both sides
could go abouttheir business ‘talking and laughing’ at these hours.
Artillery was predictablyused both at certain times and at certain
locations. So both sides couldappear to demonstrate aggression by
venturing out at certain times and tocertain locations, knowing that
the shells would fall predictably close to, butnot on, their chosen
route. Likewise, it was not considered ‘etiquette’ to fireon working
parties who had been sent out to repair a position or collect thedead
and so on.

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For instance, it is sometimes argued that thenorms of Confucian
societies enable those economies to solve the prisoners’dilemma/free
rider problems within companies without costly contracting
andmonitoring activity and that this explains, in part, the economic
success ofthose economies (see Hargreaves Heap, 1991, Casson, 1991,
North, 1991).Akerlof ’s (1983) discussion of loyalty filters, where he
explains the relativesuccess of Quaker groups in North America by their
respect for the norm ofhonesty, is another example—

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Wittgenstein of Philosophical Investigations1 is an obvious source for
this viewbecause he would deny that the meaning of something like a
person’sinterests or desires can be divorced from a social setting; and
this is a usefulopportunity to take that argument further. The
attribution of meaningrequires language rules and it is impossible to
have a private language. Thereis a long argument around the possibility
or otherwise of private languagesand it may be worth pursuing the point
in a slightly different way by askinghow agents have knowledge of what
action will satisfy the condition ofbeing instrumentally rational. Any
claim to knowledge involves a firstunquestioned premise: I know this
because I accept x. Otherwise an infiniteregress is inevitable: I
accept x because I accept y and I accept ybecause…and so on.
Accordingly, if each person’s knowledge of what isrational is to be
accessible to one another, then they must share the samefirst premises.
It was Wittgenstein’s point that people must share somepractices if
they are to attach meaning to words and so avoid the problem ofinfinite
redescription which comes with any attempt to specify the rules
forapplying the rules of a language.

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There is another similarity and difference which might also be
usefullymarked. To make it very crudely one might draw an analogy
between thedifficulty which Wittgenstein encounters over knowledge
claims and a similardifficulty which Simon (1982) addresses. (Herbert
Simon is well known ineconomics for his claim that agents are
procedurally rational, or boundedlyrational, because they do not have
the computing capacity to work out whatis the best to do in complex
settings.) To be sure, Wittgenstein finds theproblem in an infinite
regress of first principles while Simon finds thedifficulty in the
finite computing capacity of the brain. Nevertheless, both

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discussion of the Harsanyi doctrine because a similar claim seems to
underpinthat doctrine. Namely that all rational individuals must come
to the sameconclusion when faced by the same evidence. Wittgenstein
would agree to theextent that some such shared basis of interpretation
must be present ifcommunication is to be possible. But he would deny
that all societies andpeoples will share the same basis for
interpretations. The source of the sharingfor Wittgenstein is not some
universal ‘rationality’, as it is for Harsanyi; ratherit is the
practices of the community in which the people live, and these willvary
considerably across time and space.

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let us make the view inspired by Wittgensteinvery concrete. The
suggestion is that what is instrumentally rational is notwell defined
unless one appeals to the prevailing norms of behaviour. Thismay seem a
little strange in the context of a prisoners’ dilemma where thedemands
of instrumental rationality seem plain for all to see: defect! But,in
reply, those radically inspired by Wittgenstein would complain that
thenorms have already been at work in the definition of the matrix and
itspay-offs because it is rare for any social setting to throw up
unvarnishedpay-offs. A social setting requires interpretation before
the pay-offs can beassigned and norms are implicated in those
interpretations. (See forexample Polanyi (1945) who argues, in his
celebrated discussion of the riseof industrial society, that the
incentives of the market system are onlyeffective when the norms of
society place value on private materialadvance.)

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The last reflection on rationality comes from David Gauthier. He
remainsfirmly in the instrumental camp and ambitiously argues that its
dictates havebeen wrongly understood in the prisoners’ dilemma game.
Instrumental rationalitydemands cooperation and not defection! To make
his argument he distinguishesbetween two sorts of maximisers: a
straightforward maximiser (SM) and aconstrained maximiser (CM). A
straightforward maximiser defects (D)following the same logic that we
have used so far. The constrained maximiseruses a conditional strategy
of cooperating (C) with fellow constrainedmaximisers and defecting with
straightforward maximisers. He then asks:which disposition
(straightforward or constrained) should an instrumentallyrational
person choose to have? (The decision can be usefully compared with
asimilar one confronting Ulysses in connection with listening to the
Sirens,

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The point is that if instrumental rationality is what motivates the CM
inthe prisoners’ dilemma, then a CM must want to defect

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In other words, being a CM may be better than beingan SM, but the best
strategy of all is to label yourself a CM and then cheaton the deal.
And, of course, when people do this, we are back in a worldwhere
everyone defects.

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Surely, this line of argument goes,it pays not to ‘zap’ a fellow CM
because your reputation as a CM is therebypreserved and this enables
you to interact more fruitfully with fellow CMs inthe future. Should
you zap a fellow CM now, then everyone will know that youare a rogue
and so in your future interactions, you will be treated as an SM.
Inshort, in a repeated setting, it pays to forgo the short run gain
from defectingbecause this ensures the benefits of cooperation over the
long run. Thusinstrumental calculation can make true CM behaviour the
best course ofaction.

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Moreover, it achieved aremarkable degree of cooperation.

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each program.Tit-for-Tat, submitted by Anatol Rapoport, won the
tournament. Theprogram starts with a cooperative move and then does
whatever theopponent did on the previous move. It was, as Axelrod
points out, not onlythe simplest program, it was also the best!

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dilemma can be defeated without the intervention of a collective agency
likethe State—that is, provided the interaction is repeated
sufficiently often tomake the long term benefits outweigh the short
gains.

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‘Is the Prisoners’ dilemma all of sociology?’Of course, it is not, he
answers. Nevertheless, it has fascinated social scientistsand proved
extremely difficult to unlock in one-shot plays of the game—atleast,
without the creation of a coercive agency like the State which is
capableof enforcing a collective action or without the introduction of
norms or somesuitable form of moral motivation on the part of the
individuals playing thegame. Of course, many interactions are repeated
and so this stark conclusionmay be modified by the discussion of the
next chapter.

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Perhaps somewhat surprisingly, mutualdefection remains the only Nash
equilibrium. The following two sectionsdiscuss, respectively,
indefinitely repeated prisoners’ dilemma and therelated free rider
games. We show (section 6.4) that mutual cooperation isa possible Nash
equilibrium outcome in these games provided there is a‘sufficient’
degree of uncertainty over when the repetition will cease.There are
some significant implications here both for liberal politicaltheory and
for the explanatory power of game theory. We notice that thisresult
means that mutual cooperation might be achieved without theintervention
of a collective agency like the State and/or withoutappealing to some
expanded notion of rational agency

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the absence of a theory of equilibriumselection.

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Firstly, it provides a theoretical warrant for the belief that
cooperation in theprisoners’ dilemma can be rationally sustained
without the intervention ofsome collective agency like the State,
provided there is sufficient (to be definedlater) doubt over when the
repeated game will end. Thus the presence of aprisoners’ dilemma
interaction does not necessarily entail either a poor socialoutcome or
the institutions of formal collective decision making. The
thirdalternative is for players to adopt a tit-for-tat strategy
rationally.1 If they adoptthis third alternative the socially inferior
outcome of mutual defection will beavoided without the interfering
presence of the State or some other formal(coercive) institution.

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Equally, it is probable that both prisonersin the original example may
think twice about ‘confessing’ because each knowsthat they are likely
to encounter one another again (if not in prison, at leastoutside) and
so there are likely to be opportunities for exacting ‘punishment’ ata
later date.

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Folk theorem

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This is an extremely important result for the social sciences because
itmeans that there are always multiple Nash equilibria in such
indefinitelyrepeated games. Hence, even if Nash is accepted as the
appropriateequilibrium concept for games with individuals who are
instrumentally rationaland who have common knowledge of that
rationality, it will not explain howindividuals select their strategies
because there are many strategy pairs whichform Nash equilibria in
these repeated games. Of course, we have encounteredthis problem in
some one-shot games before, but the importance of this resultis that it
means the problem is always there in indefinitely repeated games.Even
worse, it is amplified by repetition. In other words, game theory needs
tobe supplemented by a theory of equilibrium selection if it is to
explain actionin these indefinitely repeated games, especially if it is
to explain howcooperation actually arises spontaneously in indefinitely
repeated prisoners’dilemma games.

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Now consider a tit-for-tat strategy in this group which works in
thefollowing way. The strategy partitions the group into those who are
in ‘goodstanding’ and those who are in ‘no standing’ based on whether
the individualcontributed to the collective fund in the last time
period. Those in ‘goodstanding’ are eligible for the receipt of help
from the group if they fall ‘ill’ thistime period, whereas those who
are in ‘no standing’ are not eligible for help.Thus tit-for-tat
specifies cooperation and puts you in ‘good standing’ for thereceipt of
a benefit if you fall ‘ill’ (alternatively, to connect with the
earlierdiscussion, one might think of cooperating as securing a
‘reputation’ whichputs one in ‘good standing’

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Notice your decision now will determine whether you are in ‘good
standing’from now until the next opportunity that you get to make this
decision (whichwill be the next period if you do not fall ‘ill’ or the
period after that if you fall‘ill’). So we focus on the returns from
your choice now until you next get theopportunity to choose.

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Who needs the State?

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Here we pick up threads of the Hobbesianargument for the State and see
what the result holds for this argument. At firstglance, the argument
for the State seems to be weakened because it appearsthat a group can
overcome the free rider problem without recourse to theState for
contract enforcement. So long as the group can punish free riders
byexcluding them from the benefits of cooperation (as for instance the
Pygmiespunished Cephu—see Chapter 5), then there is the possibility of
‘spontaneous’public good provision through the generalisation of the
tit-for-tat strategy.Having noted this, nevertheless, the point seems
almost immediately to beblunted since the difference between a
Hobbesian State which enforcescollective agreements and the generalised
tit-for-tat arrangement is notaltogether clear and so in proving one we
are hardly undermining the other.After all, the State merely codifies
and implements the policies of‘punishment’ on behalf of others in a
very public way (with the rituals ofpolice stations, courts and the
like). But, is this any different from the golfclub which excludes a
member from the greens when the dues have not beenpaid or the Pygmies’
behaviour towards Cephu? Or the gang which excludespeople who have not
contributed ‘booty’ to the common fund?

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Box 6.2

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contract—that the creation of the State by the individual also helps
shape asuperior individual.) Hayek, however, prefers the ‘English
tradition’ because hedoubts (a) that the formation of the State is part
of a process which liberates(and moulds) the social agent and (b) that
there is the knowledge to informsome central design so that it can
perform the task of resolving free ridingbetter than spontaneously
generated solutions (like tit-for-tat). In other words,reason should
know its limits and this is what informs Hayek’s support forEnglish
pragmatism and its suspicion of the State.Of course there is a big ‘if
in Hayek’s argument. Although Beirut stillmanaged to function without a
grand design, most of its citizens prayed forone. In short, the
spontaneous solution is not always the best. Indeed, as wehave seen,
the cooperative solution is just one among many Nash equilibria
inrepeated games, so in the absence of some machinery of collective
decisionmaking, there seems no guarantee it will be selected. Against
this, however, itis sometimes argued that evolution will favour
practices which generate thecooperative outcome since societies that
achieve cooperation in these gameswill prosper as compared with those
which are locked in mutual defection.This is the cue for a discussion
of evolutionary game theory and we shall leavefurther discussion of the
State until we turn to evolutionary game theory

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Instead the result seems important because it demythologises the
State.Firstly the State qua State (that is, the State with its police
force, its courts andthe like) is not required to intrude into every
social interaction which suffersfrom a free rider problem. There are
many practices and institutions which aresurrogates for the State in
this regard. Indeed, the Mafia has plausiblydisplaced the State in
certain areas precisely because it provides the services ofa State.
Likewise, during the long civil war years inhabitants of Beirutsomehow
still managed to maintain services which required the overcoming offree
rider problems.Secondly since something like the State as contract
enforcer might well arise‘spontaneously’ through the playing of free
rider games repeatedly, it need notrequire any grand design. There need
be no constitutional conventions. In thisway the result counts strongly
for what Hayek (1962) refers to as the Englishas opposed to the
European continental Enlightenment tradition. The latterstresses the
power of reason to construct institutions that overcome problemslike
those of the free rider. (It also often presupposes—recall Rousseau’s
social

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different if you pay the State in the form of taxes or the Mafia in the
form oftribute?

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example comes from strategicdecisions by the legislature when the
Executive is trying to push throughParliament a series of bills that
the latter is unsympathetic towards.

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President proposes legislation. The Congress is notin sympathy with the
proposal and must decide whether to make amendments.If it decides to
make an amendment, then the President must decide whetherto fight the
amendment or acquiesce. Looking at the President’s pay-offs it
isobvious that, even though he or she prefers that the Congress does
not amendthe legislation, if it does, he or she would not want to fight

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the Folk theorem ensures that aninfinity of war/acquiescence patterns
are compatible with instrumentalrationality. Nevertheless, the duration
of such games is usually finite andsometimes their length is
definite—e.g. US Presidents have a fixed term andincumbents have only a
fixed number of local markets that they wish todefend. What happens
then? Would it make sense for the President or theincumbent to put on a
show of strength early on (e.g. by fighting the Congressor unleashing a
price war) in order to create a reputation for belligerence thatwould
make the Congress and the entrant think that, in future rounds,
theywill end up with pay-off -1/2 if they dare them?

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In the finitely repeated version of the game Nash backward
inductionargues against this conclusion. Just as in the case of the
prisoners’ dilemmain the previous subsection, it suggests that, since
there will be no fighting atthe last play of the game, the reputation
of the President/incumbent willunravel to the first stage and no
fighting will occur (rationally). Theconclusion changes again once we
drop CKR (or allow for different types ofplayers).

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Of course, there may be actions that can be takenoutside the game and
which have a similar effect on the beliefs of others. Such‘signalling’
behaviour is considered briefly in this section to round out
thediscussion of reputations. It is of potential relevance not only to
repeated, butalso to one-shot games.

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when the game isrepeated and there is a unique Nash equilibrium things
change. The Nashequilibrium is attractive because as time goes by and
agents adjust theirexpectations of what others will do in the light of
experience, then they willseem naturally drawn to the Nash equilibrium
because it is the only restingplace for beliefs. Any other set of
beliefs will upset itself.

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Nevertheless, there is still no guarantee that a Nash equilibrium
willsurface even if it exists and it is unique.

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The strength of the Nash equilibrium is that forward looking agents
mayrealise that (R2, C2) is the only outcome that does not engender
such thoughts.We just saw that adaptive (or backward looking)
expectations will not do thetrick. If, however, after having been
around the pay-off matrix a few timesplayers ask themselves the
question ‘How can we reach a stable outcome?’,they may very well
conclude that the only such outcome is the Nashequilibrium (R2, C2).But
why would they want to ask such a question? What is so wrong
withinstability (and disequilibrium) after all? Indeed in the case of
Figure 2.6 ourplayers have an incentive to avoid a stable outcome
(observe that on averagethe cycle which takes them from one extremity
of the pay-off matrix toanother yields a much higher pay-off than the
Nash equilibrium result). If, onthe other hand, pay-offs were as in
Figure 6.4 below, they would be stronglymotivated to reach the Nash
equilibrium.

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It is easy to see that this type of adaptivelearning will never lead
the players to the Nash equilibrium outcome (R2, C2).Instead, they will
be oscillating between outcomes (R1, C1), (R1, C3), (R3, C1)and (R3,
C3).Can they break away from this never ending cycle and hit the
Nashequilibrium? They can provided they converge onto a common
forwardlooking train of thought. For

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Thus we conclude that whether repetition makes the Nashequilibrium more
or less likely when it is unique must depend on thecontingencies of how
people learn and the precise pay-offs from non-Nashbehaviour.

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Broadly put, this is one and the same problem. It is a problem
withspecifying how agents come to hold beliefs which are extraneous to
the game(in the sense that they cannot be generated endogenously
through theapplication of the assumptions of instrumental rationality
and commonknowledge of instrumental rationality)

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the insights of evolutionary game theory arecrucial material for many
political and philosophical debates, especially thosearound the State.

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The argument for suchan agency turns on the general problem of
equilibrium selection and on theparticular difficulty of overcoming the
prisoners’ dilemma. When there aremultiple equilibria, the State can,
through suitable action on its own part, guidethe outcomes towards one
equilibrium rather than another. Thus the problemof equilibrium
selection is solved by bringing it within the ambit of
consciouspolitical decision making. Likewise, with the prisoners’
dilemma/ free riderproblem, the State can provide the services of
enforcement. Alternativelywhen the game is repeated sufficiently and
the issue again becomes one ofequilibrium selection, then the State can
guide the outcomes towards thecooperative Nash equilibrium.

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intransigent Right’

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—that is, the idea that you can turn social outcomes intomatters of
social choice through the intervention of a collective action
agencylike the State. The positive argument against ‘political
rationalism’, as the quoteabove suggests, turns on the idea that these
interventions are not evennecessary. The failure to intervene does not
spell chaos, chronic indecision,fluctuations and outcomes in which
everyone is worse off than they couldhave been. Instead, a ‘spontaneous
order’ will be thrown up as a result ofevolutionary processes.

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Likewise, there are problems of ‘political failure’ that subvert the
ideal ofdemocratic decision making and which can match the market
failures that theState is attempting to rectify. For example, Buchanan
and Wagner (1977) andTullock (1965) argue that special interests are
bound to skew ‘democraticdecisions’ towards excessively large
bureaucracies and high governmentexpenditures. Furthermore there are
difficulties, especially after the Arrowimpossibility theorem, with
making sense of the very idea of something likethe ‘will of the people’
in whose name the State might be acting (see Arrow,1951, Riker, 1982,
Hayek, 1962, and Buchanan, 1954).1These, so to speak, are a shorthand
list of the negative arguments comingfrom the political right against
‘political rationalism’ or ‘socialconstructivism’

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Forinstance, there are problems of inadequate knowledge which can mean
thateven the best intentioned and executed political decision generates
unintendedand undesirable consequences. Indeed this has always been an
importanttheme in Austrian economics, featuring strongly in the 1920s
debate over thepossibility of socialist planning as well as
contemporary doubts over thewisdom of more minor forms of State
intervention.

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Hayek (1962) himself tracesthe battlelines in the dispute back to the
beginning of Enlightenmentthinking:Hayek distinguished two intellectual
lines of thought about freedom, ofradically opposite upshot. The first
was an empiricist, essentially Britishtradition descending from Hume,
Smith and Ferguson, and seconded byBurke and Tucker, which understood
political development as aninvoluntary process of gradual institutional
improvement, comparable tothe workings of a market economy or the
evolution of common law. Thesecond was a rationalist, typically French
lineage descending fromDescartes through Condorcet to Comte, with a
horde of modernsuccessors, which saw social institutions as fit for
premeditatedconstruction, in the spirit of polytechnic engineering. The
former lineled to real liberty; the latter inevitably destroyed it.

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evolutionary stable strategies

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In particular, wesuggest that the evolutionary approach can help
elucidate the idea that poweris mobilised through institutions and
conventions. We conclude the chapterwith a summing-up of where the
issue of equilibrium selection and the debateover the State stands
after the contribution of the evolutionary approach.

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The basic idea behind this equilibrium concept is that an ESS is a
strategywhich when used among some population cannot be ‘invaded’ by
anotherstrategy because it cannot be bested. So when a population uses
a strategy I,‘mutants’ using any other strategy J cannot get a toehold
and expand amongthat population.

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This is why evolutionary game theory assumes significance in the
debateover an active State. It should help assess the claims of
‘spontaneous order’made by those in the British corner and so advance
one of the central debatesin Enlightenment political thinking.

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This is, if youlike, a version of Hobbes’s nightmare where there are no
property rightsand everyone you come across will potentially claim your
goods.

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Secondly, and more specifically, there is the result that although the
symmetricalplay of this game yields a unique equilibrium, it becomes
unstable the momentrole playing begins and some players start to
recognise asymmetry. Sincecreative agents seem likely to experiment
with different ways of playing thegame, it would be surprising if there
was never some deviation based on anasymmetry. Indeed it would be more
than surprising because there is muchevidence to support the idea that
people look for ‘extraneous’ reasons whichmight explain what are in
fact purely random types of behaviour (see theadjacent box on winning
streaks).Formally, this leaves us with the old problem of how the
solution to thegame comes about. However, evolutionary game theory does
at least point usin the direction of an answer. The phase diagram in
Figure 7.2 reveals that theselection of an equilibrium depends
critically on the initial set of beliefs

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once animperfect form of rationality is posited. In other words, it is
not beingdeduced as an implication of the common knowledge of
rationalityassumption which has been the traditional approach of
mainstream gametheory.

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Thirdly, it can be noted that the selection of one ESS rather than
anotherembodies a convention

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To put these observationsrather less blandly, since rationality on this
account is only responsible for thegeneral impulse towards mimicking
profitable behaviour, the history of thegame depends in part on what
are the idiosyncratic and unpredictable (non-rational, one might say,
as opposed to irrational) features of individual beliefsand learning.

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Fourthly, the selection of one equilibrium rather than another
potentiallymatters rather deeply. In effect in the hawk—dove game over
contestedproperty, what happens in the course of moving to one of the
ESSs is theestablishment of a form of property rights. Either those
playing role R get theproperty and role C players concede this right,
or those playing role C get theproperty and role R players concede this
right. This is interesting not onlybecause it contains the kernel of a
possible explanation of property rights (onwhich we shall say more
later) but also because the probability of playing roleR or role C is
unlikely to be distributed uniformly over the population. Indeed,this
distribution will depend on whatever is the source of the distinction
usedto assign people to roles.

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The question, then, of how a source of differentiation gets
establishedbecomes rather important.

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Thus the behaviour at one of theseESSs is conventionally determined
and, to repeat the earlier point, we can plotthe emergence of a
particular convention with the use of this phase diagram.It will depend
both on the presumption that agents learn from experience(the rational
component of the explanation) and on the particularidiosyncratic (and
non-rational) features of initial beliefs and precise learningrules.

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After all, perhaps the presence of these conventions can only
beaccounted for by a move towards a Wittgensteinian ontology, in which
casemainstream game theory’s foundations look decidedly wobbly. To
prevent thisdrift a more robust response is required.The alternative
response is to deny that the appeal to shared prominenceor salience
involves either an infinite regress or an acknowledgement
thatindividuals are necessarily ontologically social

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There is a further and deeper problem with the concept of salience
basedon analogy because the attribution of terms like ‘possession’
plainly begs thequestion by presupposing the existence of some sort of
property rights in thepast. In other words, people already share a
convention in the past and this isbeing used to explain a closely
related convention in the present. Thus we havenot got to the bottom of
the question concerning how people come to holdconventions in the first
place.3

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So, of course, we cannot hope to explainhow they actually achieve a new
coordination without appealing to thosebackground conventions. In this
sense, it would be foolish for socialscientists (and game theorists, in
particular) to ignore the social context inwhich individuals play new
games.

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This conclusion reinforces the earlier result that the course of
historydepends in part on what seem from the instrumental account of
rationalbehaviour to be non-rational (and perhaps idiosyncratic) and
thereforefeatures of human beliefs and action which are difficult to
predict

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mechanically. One can interpret this in the spirit of
methodologicalindividualism at the expense of conceding that
individuals are, in this regard,importantly unpredictable. On the one
hand, this does not look good for theexplanatory claims of the theory.
On the other hand, to render theindividuals predictable, it seems that
they must be given a shared history andthis will only raise the
methodological concern again of whether we canaccount for this sharing
satisfactorily without a changed ontology. Insummary, if individuals
are afforded a shared history, then social context is‘behind’ no one
and ‘in’ everyone and then the question is whether it is agood idea to
analyse behaviour by assuming (as methodological individualistsdo) the
separability of context and action.4

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The underlying point here is that discrimination may be
evolutionarystable if the dominated cannot find ways of challenging the
social conventionthat supports their subjugation. This conclusion is
not necessarily rightbecause there are other potential sources of
change. The insight that we preferto draw is that individual attempts
to buck an established convention areunlikely to succeed, whereas the
same is not true when individuals takecollective action.

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Stasis, status quo: Thus the introduction of a convention will benefit
the average person, butif you happen to be so placed with respect to
the convention that you onlyplay the dominant role with a probability
of less than 1/3, then you would bebetter off without the convention.
This result may seem puzzling at first: whydo the people who play a
dominant role less than 1/3 of the time not revert tothe symmetric play
of the game and so undermine the convention? The answeris that even
though the individual would be better off if everyone quit
theconvention, it does not make sense to do so individually. After all,
aconvention will tell your opponent to play either H or D, and then
instruct youto play D or H respectively; and you can do no better than
follow thisconvention since the best reply to H remains D and likewise
the best reply toD is H. It is just tough luck if you happen to get the
D instruction all thetime!We take the force of this individual
calculation to be a powerful contributorto the status quo and it might
seem to reveal that evolutionary processes yieldto stasis.

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Conventions, inequality and revolt

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To summarise, we should expect a convention to emerge even though itmay
not suit everyone, or indeed even if it short-changes the majority. It
maybe discriminatory, inequitable, non-rational, indeed thoroughly
disagreeable, yetsome such convention is likely to arise whenever a
social interaction like hawk-dove is repeated. Which convention emerges
will depend on the sharedsalience of extraneous features of the
interaction, initial beliefs and the waythat people learn.

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Standstill: A potential weakness of evolutionary game theory has just
becomeapparent. Once the bandwagon has come to a standstill, and one
conventionhas been selected, the theory cannot account for a potential
subversion of theestablished convention. Such an account would require,
as we argued in theprevious paragraph, an understanding of political
(that is, collective) actionbased on a more active form of human agency
than the one provided byinstrumental rationality. Can evolutionary game
theory go as far?

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Recall the idea of a trembling hand in section 2.7.1 and suppose
thatplayers make mistakes sometimes. In particular, when they intend
tocooperate they occasionally execute the decision wrongly and they
defect. Inthese circumstances, playing t punishes you for the mistake
endlessly becauseit means that your opponent defects next round in
response to your mistakendefection. If in the next period you
cooperate, you are bound to get zapped.If you follow your t-strategy
next time, then you will be defecting while youropponent will be
cooperating and a frustrating sequence of alternatingdefections and
cooperations will ensue. One way out of this bind is toamend t to t’
whereby, if you defect by mistake, then you cooperate twiceafterwards:
the first time as a gesture of acknowledging your mistake and thesecond
in order to coordinate your cooperative behaviour with that of
youropponent. In other words, the amended tit-for-tat instructs you to
cooperatein response to a defection which has been provoked by an
earlier mistakendefection on your part.

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Eventhough strategy C would do equally well as a reply to t’, if your
opponentmade the mistake (last period) then you know that your opponent
willcooperate in the next two rounds no matter what you do this period.
Thusyour best response in this round is to defect

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Conventions as covert social power

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even more covert power that comes from being able to mould the
preferencesand the beliefs of others so that a conflict of interest is
not even latentlypresent.

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with the interests of another.It is common in discussions of power to
distinguish between the overt andthe covert exercise of power. Thus,
for instance, Lukes (1974) distinguishesthree dimensions of power.
There is the power that is exercised in the politicalor the economic
arena where individuals, or firms, institutions, etc., are able
tosecure decisions which favour their interests over others quite
overtly. This isthe overt exercise of power along the first dimension.
In addition, there is themore covert power that comes from keeping
certain items off the politicalagenda. Some things simply do not get
discussed in the political arena and inthis way the status quo
persists. Yet the status quo advantages some rather thanothers and so
this privileging of the status quo by keeping certain issues offthe
political agenda is the second dimension of power. Finally, there is
the

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The figure of Spartacus captured imaginations over theages, not so much
because of his military antics, but because he personifiedthe
possibility of liberating the slaves from the beliefs which sustained
theirsubjugation.

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this is the power which works through the mind and which dependsfor its
influence on the involvement or agreement of large numbers of
thepopulation (again connecting with the earlier observation about the
force ofcollective action).

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State were consciously to select a convention in these circumstances
thenwe might observe the kind of political haggling associated with the
overtexercise of power. Naturally when a convention emerges
spontaneously, we donot observe this because there is no arena for the
haggling to occur, yet theemergence of a convention is no less decisive
than a conscious politicalresolution in resolving the conflict of
interest.6Evolutionary game theory also helps reveal the part played by
beliefs,especially the beliefs of the subordinate group, in securing
the power of thedominant group (a point, for example, which is central
to Gramsci’s notion ofhegemony and Hart’s contention that the power of
the law requires voluntarycooperation).

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Theannexing of virtue can happen as a result of well-recognised
patterns ofcognition.

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Of course, like all theories of cognitive dissonance removal,this story
begs the question of whether the adjustment of beliefs can do thetrick
once one knows that the beliefs have been adjusted for the
purpose.Nevertheless, there seem to be plenty of examples of dissonance
removal

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Our final illustration of how evolutionary game theory might help
sharpenour understanding of debates around power in the social sciences
relates tothe question of how gender and race power distributions are
constitutedand persist. The persistence of these power imbalances is a
puzzle to some.

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Once a convention isestablished in this game, a set of property
relations are also established.Hence the convention could encode a set
of class relations for this gamebecause it will, in effect, indicate
who owns what and some may end upowning rather a lot when others own
scarcely anything. However, as wehave seen a convention of this sort
will only emerge once the game isplayed asymmetrically and this
requires an appeal to some piece ofextraneous information like sex or
age or race, etc. In short, the creationof private property relations
from the repeated play of these gamesdepends on the use of some other
asymmetry and so it is actuallyimpossible to imagine a situation of
pure class relations, as they couldnever emerge from an evolutionary
historical process. Or to put thisslightly differently: asymmetries
always go in twos!This understanding of the relation has further
interesting implications.For instance, an attack on gender
stratification is in part an attack on classstratification and vice
versa.

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Likewise, however, it would be wrong toimagine that the attack on
either if successful would spell the end of theother.

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On this account of powerthrough the working of convention, the
ideological battle aimed atpersuading people not to think of themselves
as subordinate is half thebattle because these beliefs are part of the
way that power is mobilised.

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. The feedback mechanism, however, ispresent in this analysis and it
arises because there is ‘learning’. It is theassumption that people
shift towards practices which secure better outcomes(without knowing
quite why the practice works for the best) which is thefeedback
mechanism responsible for selecting the practices. Thus in the
debateover functional explanation, the analysis of evolutionary games
lends supportto van Parijs’s (1982) argument that ‘learning’ might
supply the generalfeedback mechanism for the social sciences which will
license functionalexplanations in exactly the same way as natural
selection does in the biologicalsciences.

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effect, the explanation of gender and racial inequalities using
thisevolutionary model is an example of functional argument.

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The differencebetween men and women or between whites and blacks has no
merit inthe sense that it does not explain why the differentiation
persists. Thedifferentiation has the unintended consequence of helping
the populationto coordinate its decision making in settings where there
are benefitsfrom coordination. It is this function of helping the
population to selectan equilibrium in a situation which would otherwise
suffer from theconfusion of multiple equilibria which explains the
persistence of thedifferentiation.

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So far, however, the difference between the two camps (H&EVGT andMarx)
is purely based on value judgements: one argues that illusory moralsare
good for all, the other that they are not. In this sense, both
canprofitably make use of the analysis in evolutionary game theory.
Indeed, aswe have already implied in section 7.3.4, a radical political
project grounded

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On the side of H&EVGT, Hume thinks that suchillusions play a positive
role (in providing the ‘cement’ which keeps societytogether) in
relation to the common good. So do neo-Humeans (like Sugden)who are, of
course, less confident that invocation of the ‘common good’ is agood
idea (as we mentioned in section 7.6.2) but who are still happy to
seeconventions (because of the order they bring) become entrenched in
sociallife even if this is achieved with the help of a few moral
‘illusions’. On theother side, however, Marx insists that moral
illusions are never a good idea(indeed he dislikes all illusions).
Especially since, as he sees it, their socialfunction is to help some
dreadful conventions survive (recall how in section7.3.4 we showed that
disagreeable conventions may become stable even ifthey are detrimental
to the majority). Marx believed that we can

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which sound quite like observations that Marxists might make:
theimportance of taking collective action if one wants to change a
convention;how power can be covertly exercised; how beliefs
(particularly moral beliefs)may become endogenous to the conventions we
follow; how propertyrelations might develop functionally; and so on.

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Indeedmost of the ideas developed on the basis of H&EVGT in the
precedingpages would find Marx in agreement.

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People may think that their beliefson such matters go beyond material
values (i.e. self-interest, which in ourcontext means pay-offs); that
they respond to certain universal ideals aboutwhat is ‘good’ and
‘right’, when all along their moral beliefs are a direct(even if
unpredictable) repercussion of material conditions and interests.

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An analysis of hawk—dove games, along the lines of H&EVGT, helpsexplain
the evolution of property rights in primitive societies. Once
theserights are in place and social production is under way, each group
in society(e.g. the owners of productive means, or those who do not own
tools, land,machines, etc.) develops its own interest. And since (as
H&EVGT concurs)conventions evolve in response to such interests, it is
not surprising thatdifferent conventions are generated within different
social groups in responseto the different interests. The result is
conflicting sets of conventions which

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Finally, the established (stable) conventions acquire moral weight and
even leadpeople to believe in something called the common good—which is
most likelyanother illusion

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In summary, H&EVGTbegins with a behavioural theory based on the
individual interest and eventuallylands on its agreeable by-product:
the species interest. There is nothing inbetween the two types of
interest. By contrast, Marx posits another type ofinterest in between:
class interest.Marx’s argument is that humans are very different from
other speciesbecause we produce commodities in an organised way before
distributingthem. Whereas other species share the fruits of nature
(hawk—dove games aretherefore ‘naturally’ pertinent in their state of
nature), humans have developedcomplex social mechanisms for producing
goods. Naturally, the norms ofdistribution come to depend on the
structure of these productive mechanisms.They involve a division of
labour and lead to social divisions (classes). Whichclass a person
belongs to depends on his or her location (relative to others)within
the process of production. The moment collective production (as in
thecase of Cephu and his tribe in Chapter 5) gave its place to a
separationbetween those who owned the tools of production and those who
workedthose tools, then groups with significantly different (and often
contradictory)interests developed.

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in collective action is as compatible with evolutionary game theory as
is theneo-Humeanism of Sugden (1986, 1989). But is there something more
inMarx than a left wing interpretation of evolutionary game theory? We
thinkthere is.

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lead to conflicting morals. Each set of morals becomes an ideology.9
Which setof morals (or ideology) prevails at any given time? Marx
thinks that, inevitably,the social class which is dominant in the
sphere of production and distributionwill also be the one whose set of
conventions and morals (i.e. whose ideology)will come to dominate over
society as a whole.To sum up Marx’s argument so far, prevailing moral
beliefs are illusoryproducts of a social selection process where the
driving force is not somesubjective individual interest but objective
class interest rooted in thetechnology and relations of production.
Although there are many conflictingnorms and morals, at any particular
time the morality of the ruling class isuniquely evolutionary stable.
The mélange of legislation, moral codes, norms,etc., reflects this
dominant ideology.But is there a fundamental difference between the
method of H&EVGTand Marx? Or is it just a matter of introducing classes
in the analysiswithout changing the method?

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So, how would Marx respond to evolutionary game theory if he werearound
today? He would, we think, be very interested in some of the
radicalconclusions in this chapter. However, he would also speak
derisively of thematerialism of H&EVGT Marx habitually poured scorn on
those (e.g.Spinoza and Feuerbach) who transplanted models from the
natural sciencesto the social sciences with little or no modification
to allow for the fact thathuman beings are very different to atoms,
planets and molecules.12 Wemention this because at the heart of H&EVGT
lies a simple Darwinianmechanism (witness that there is no analytical
difference between the modelsin the biology of John Maynard Smith and
the models in this chapter). Marxwould probably claim that the theory
is not sufficiently evolutionary because(a) its mechanism comes to a
standstill once a stable convention has evolved,and (b) of its reliance
on instrumental rationality which reduces humanactions to passive
reflex responses to some (meta-physical) self-interest.

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Especially in hisphilosophical (as opposed to economic) works, Marx
argued strongly for anevolutionary (or more precisely historical)
theory of society with a modelof human agency which retains human
activity as a positive (creative) forceat its core. In addition, Marx
often spoke out against mechanism; againstmodels borrowed directly from
the natural sciences (astronomy andbiology are two examples that he
warned against). It is helpful to preservesuch an aversion since humans
are ontologically different to atoms andgenes. Of course Marx himself
has been accused of mechanism and,indeed, in the modern (primarily
Anglo-Saxon) social theory literature he istaken to be an exemplar of
19th century mechanism. Nevertheless hewould deny this, pointing to the
dialectical method he borrowed fromHegel and which (he would claim)
allowed him to have a scientific, yetnon-mechanistic, outlook. Do we
believe him? As authors we disagree here.SHH does not, while YV does.

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Of course there is always the answer that self-interest feeds into
moral beliefsand then moral beliefs feed back into self-interest and
alter people’s desires.And so on. But that would be too circular for
Marx. It would not explainwhere the process started and where it is
going. By contrast, his version ofmaterialism (which he labelled
historical materialism) starts from thetechnology of production and the
corresponding social organisation. Thelatter entails social classes
which in turn imbue people with interests; peopleact on those interests
and, mostly without knowing it, they shape theconventions of social
life which then give rise to morals. The process,however, is grounded
on the technology of production at the beginning of thechain. And as
this changes (through technological innovations) it provides theimpetus
for the destabilisation of the (temporarily) evolutionary
stableconventions at the other end of the chain.

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Ifmorals are socially manufactured, then so is self-interest.

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Perhaps our disagreement needs to be understood in terms of thelack of
a shared history in relation to these debates—one of us embarkingfrom
an Anglo-Saxon, the other from a (south) European, tradition. It
was,after all, one of our important points in earlier chapters that
game theoristsshould not expect a convergence of beliefs unless agents
have a sharedhistory!

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most of the population. This would seem to provide ammunition for the
socialconstructivists, but of course it depends on them believing that
collectiveaction agencies like the State will have sufficient
information to distinguish thesuperior outcomes. Perhaps all that can
be said on this matter is that, if youreally believe that evolutionary
forces will do the best that is possible, then it isbeyond dispute that
these forces have thrown up people who are predisposedto take
collective action. Thus it might be argued that our
evolutionarysuperiority as a species derives in part precisely from the
fact that we are pro-active through collective action agencies rather
than reactive as we would beunder a simple evolutionary scheme.

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Turning to another dispute, that between social constructivism and
spontaneousorder within liberal political theory, two clarifications
have occurred. The first isthat there can be no presumption that a
spontaneous order will deliveroutcomes which make everyone better off,
or even outcomes which favour

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Thesetheoretical moves will threaten to dissolve the distinction
between action andstructure which lies at the heart of the game
theoretical depiction of social lifebecause it will mean that the
structure begins to supply reasons for action andnot just constraints
upon action. On the optimistic side, this might be seen asjust another
example of how discussions around game theory help to dissolvesome of
the binary oppositions which have plagued some debates in
socialscience—just as it helped dissolve the opposition between gender
and classearlier in this chapter. However, our concern here is not to
point to requiredchanges in ontology of a particular sort. The point is
that some change isnecessary, and that it is likely to threaten the
basic approach of game theory tosocial life.

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Secondly, on the difficult cases where equilibrium selection
involveschoices over whose interests are to be favoured (i.e. it is not
a matter ofselecting the equilibrium which is better for everyone),
then it is notobvious that a collective action agency like the State is
any better placed tomake this decision than a process of spontaneous
order. This may come asa surprise, since we have spent most of our time
here focusing on theindeterminacy of evolutionary games when agents are
only weaklyinstrumentally rational.

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In other words the very debate within liberal political theory over
socialconstructivism versus spontaneous order is itself unable to come
to aresolution precisely because its shared ontological foundations are
inadequatefor the task of social explanation. In short, we conclude
that not only willgame theory have to embrace some expanded form of
individual agency, if itis to be capable of explaining many social
interactions, but also that this isnecessary if it is to be useful to
the liberal debate over the scope of theState.

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sabotage

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What it does mean is thatour interpretation of results must be cautious
and that, ultimately,laboratory experiments may only be telling us how
people behave inlaboratories.

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becausethere are some players who are unconditionally cooperative or
‘altruistic’ in theway that they play this game and, secondly, because
whether someone iscooperative or not seems to be determined by one’s
background, rather thanby how clever (or rational) he or she is (see
adjacent box on the curse ofeconomics). In this sense, the evidence
seems to point to a falsification of theassumption of instrumentally
rational action based on the pay-offs

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divisions of an army are stationed on two hill-tops overlooking a
valley inwhich an enemy division can be clearly seen. It is known that
if both divisionsattack simultaneously they will capture the enemy with
none, or very little, lossof life. However, there were no prior plans
to launch such an attack, as it wasnot anticipated that the enemy would
be spotted in that location. How will thetwo divisions coordinate their
attack (we assume that they must maintain visualand radio silence)?
Neither commanding officer will launch an attack unless heis sure that
the other will attack at the same time. Thus a classic
coordinationproblem emerges.Imagine now that a messenger can be sent
but that it will take him about anhour to convey the message. However,
it is also possible that he will be caughtby the enemy in the meantime.
If everything goes smoothly and the messengergets safely from one
hill-top to another, is this enough for a coordinated attackto be
launched? Suppose the message sent by the first commanding officer
tothe second read: ‘Let’s attack at dawn!’ Will the second officer
attack at dawn?No, unless he is confident that the first commanding
officer (who sent the

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message) knows that the message has been received. So, the
secondcommanding officer sends the messenger back to the first with the
message:‘Message received. Dawn it is!’ Will the second officer attack
now? Not untilhe knows that the messenger has delivered his message.
Paradoxically, noamount of messages will do the trick since
confirmation of receipt of the lastmessage will be necessary regardless
of how many messages have been alreadyreceived.

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We see that in a coordination game like the above, even a very
highdegree of common knowledge of the plan to attack at dawn is not
enough toguarantee coordination (see Box 8.3 for an example of how
different degreesof common knowledge can be engendered in the
laboratory). What is needed(at least in theory) is a consistent
alignment of beliefs (CAB) about the plan.1And yet this does not
exclude the possibility that the two commandingofficers will both
attack at dawn with very high probability. How successfullythey
coordinate will, however, depend on more than a high degree ofcommon
knowledge. Indeed the latter may even be un-necessary providedthe time
of the attack is carefully chosen. The classic early experiments
byThomas Schelling on behaviour in coordination games have confirmed
this—

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Thus in experiments, Pareto superiority does not seem to be a
generalcriterion which players use to select between Nash equilibria
(see also Chapter7). In conclusion, so far it seems that the way people
actually play these gamesis neither directly controlled by the
strategic aspects of the game (i.e. thelocation of the best response
marks (+) and (-) in the matrix) nor by the size ofthe return from
coordinating on non-Nash outcomes such as (R3, C3): it is
aso-far-unexplained mixture of the two factors that decides.

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To phrase this conclusion slightly differently, but in a way which
connectswith the results in the next section, bargaining is a ‘complex
socialphenomenon’ where people take cues from aspects of their social
life whichgame theory typically overlooks. Thus players seem to base
their behaviouron aspects of the social interaction which game theory
typically treats asextraneous; and when players share these extraneous
reference points such

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What we have here is an evolution ofsocial roles. Players with the R
label develop a different attitude towardsreflective cooperation to
those players with the C role in spite of the fact that theRs and the
Cs are the same people. In other words, the signal which causes
theobserved pattern of cooperation seems to be emitted by the label R
or C. Thisreminds us of the discussion in Chapter 7 about the capacity
of sex, race andother extraneous features to pin down a convention on
which the structure ofdiscrimination is grounded.

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Experimentation with game theory is good, clean fun. Can it be more
thanthat? Can it offer a way out of the obtuse debates on CKR, CAB,
NEMS,Nash backward induction, out-of-equilibrium behaviour, etc.? The
answerdepends on how we interpret the results. And as interpretation
leaves plentyof room for controversy, we should not expect the data
from the laboratoryunequivocally to settle any disputes. Our suspicion
is that experiments are togame theory what the latter is to liberal
individualism: a brilliant means ofcodifying its problems and of
creating a taxonomy of time-honoureddebates.There are, however,
important benefits from experimenting. Watchingpeople play games
reminds us of their inherent unpredictability, their sense offairness,
their complex motivation—of all those things that we tend to forgetwhen
we model humans as bundles of preferences moving around some pay-

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radical breakwith the exclusive reliance of instrumental rationality is
also necessary.

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At root we suspect that the major problem is the one that the
experimentsin the last chapter isolate: namely, that people appear to
be more complexlymotivated than game theory’s instrumental model allows
and that a part ofthat greater complexity comes from their social
location.We do not regard this as a negative conclusion. Quite the
contrary, it standsas a challenge to the type of methodological
individualism which has had afree rein in the development of game
theory.

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Along the way to this conclusion, we hope also that you have had
fun.Prisoners’ dilemmas and centipedes are great party tricks. They are
easy todemonstrate and they are amenable to solutions which are
paradoxical enoughto stimulate controversy and, with one leap of the
liberal imagination, theaudience can be astounded by the thought that
the fabric of society (even theexistence of the State) reduces to these
seemingly trivial games—Fun andGames, as the title of Binmore’s (1992)
text on game theory neatly puts it. Butthere is a serious side to all
this. Game theory is, indeed, well placed toexamine the arguments in
liberal political theory over the origin and the scopeof agencies for
social choice like the State. In this context, the problems whichwe
have identified with game theory resurface as timely warnings of
thedifficulties any society is liable to face if it thinks of itself
only in terms ofliberal individualism.

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The ambitious claim that game theory will provide a unified foundation
for allsocial science seems misplaced to