diff --git a/books/economics/game-theory-critical-introduction.md b/books/economics/game-theory-critical-introduction.md new file mode 100644 index 0000000000000000000000000000000000000000..6c35d8a0300eff1750ee58974a2781d9bc31581f --- /dev/null +++ b/books/economics/game-theory-critical-introduction.md @@ -0,0 +1,428 @@ +[[!meta title="Game Theory: a Critical Introduction"]] + +## 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. + +# 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 + + [...] + + 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. In fact this need entail no more than a simple consistency of the + +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?).