The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to do (...) by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...) game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

The paper points out that in dynamic games a player may be better-off if other players do not know his choice of strategy. That is, a player may benefit by not revealing (or not pre-determining) the choice of his action in an information set he (thereby) hopes will not be reached. He would be better-off by exercising his ``right to remain silent'' if he believes –- as the empirical evidence shows –- that players display aversion to ``Knightian uncertainty''. In this (...) case, a player who behaves strategically, may wish to avoid revealing his strategy. This is true under various interpretations of the notion of ``strategy profiles''. (shrink)

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept (...) are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi, see also Rubinstein, and Aumann and Brandenburger, a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others. (shrink)

According to a familiar argument, iterated prisoner's dilemmas of known finite lengths resolve for ideally rational and well-informed players: They would defect in the last round, anticipate this in the next to last round and so defect in it, and so on. But would they anticipate defections even if they had been cooperating? Not necessarily, say recent critics. These critics "lose" the backward-induction paradox by imposing indicative interpretations on rationality and information conditions. To regain it I propose subjunctive interpretations. To (...) solve it I stress that implications for ordinary imperfect players are limited. (shrink)

This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that (...) discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, infinite regress arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this dissertation provides the Failure Theory with the same tools. (shrink)

Professor Hausman has written an interesting and instructive book. Though I am by no means favourably disposed to methodology for economists,, I found reading Hausman enjoyable and I came away having learned things worth learning. But not all is well, largely because Hausman is a philosopher first and an economist a poor second. There are also important questions where one would have expected philosophic help which are not asked at all.

Two justifications of backward induction (BI) in generic perfect information games are formulated using Bonanno's (1992; Theory and Decision 33, 153) belief systems. The first justification concerns the BI strategy profile and is based on selecting a set of rational belief systems from which players have to choose their belief functions. The second justification concerns the BI path of play and is based on a sequential deletion of nodes that are inconsistent with the choice of rational belief functions.

The various behavioral disciplines model human behavior in distinct and incompatible ways. Yet, recent theoretical and empirical developments have created the conditions for rendering coherent the areas of overlap of the various behavioral disciplines. The analytical tools deployed in this task incorporate core principles from several behavioral disciplines. The proposed framework recognizes evolutionary theory, covering both genetic and cultural evolution, as the integrating principle of behavioral science. Moreover, if decision theory and game theory are broadened to encompass other-regarding preferences, they (...) become capable of modeling all aspects of decision making, including those normally considered “psychological,” “sociological,” or “anthropological.” The mind as a decision-making organ then becomes the organizing principle of psychology. (Published Online April 27 2007) Key Words: behavioral game theory; behavioral science; evolutionary theory; experimental psychology; gene-culture coevolution; rational actor model; socialization. (shrink)

The paper begins by providing a game-theoretic reconstruction of Gilbert’s (1989) philosophical critique of Lewis (1969) on the role of salience in selecting conventions. Gilbert’s insight is reformulated thus: Nash equilibrium is insufficiently powerful as a solution concept to rationalize conventions for unboundedly rational agents if conventions are solutions to the kinds of games Lewis supposes. Both refinements to NE and appeals to bounded rationality can plug this gap, but lack generality. As Binmore (this issue) argues, evolutive game theory readily (...) explains the origin of conventional behavior, but that is not Lewis’s project. Gilbert’s critique is generalized by reference to Bacharach’s (2006) work on team reasoning in games. The paper then argues that although Lewis’s account of the rationalization of conventions is shown by the reconstruction of Gilbert’s critique to be incomplete, Gilbert is wrong to conclude that classical (‘eductive’) game theory lacks the resources to explain conformity to conventions among people. A game-theoretic account of the dynamics of socialization, based on Ross’s (2005, 2006) idea of ‘game determination’, rationalizes choices of conventional strategies in overlapping generations contexts, provided agents are products of evolutionary selection and know that other players are also such products. (shrink)

In the standard money pump, an agent with cyclical preferences can avoid exploitation if he shows foresight and solves his sequential decision problem using backward induction (BI). This way out is foreclosed in a modified money pump, which has been presented in Rabinowicz (2000). There, BI will lead the agent to behave in a self-defeating way. The present paper describes another sequential decision problem of this kind, the Centipede for an Intransitive Preferrer, which in some respects is even more striking (...) than the modified pump. In the new problem, the BI reasoning that implies self-defeating behavior does not rest on the controversial robustness assumption concerning beliefs in one's future rationality. This strengthens the claim that foresight cannot save the intransitive preferrer from a self-defeating course of action. (shrink)

Many different arguments against the possibility of perfect rationality have appeared in the literature, and these target several different conceptions of perfect rationality. It is not clear how these different conceptions of perfect rationality are related, nor is it clear how the arguments showing their impossibility are related, and it is especially unclear what the impossibility results show when taken together. This paper gives an exposition of the different conceptions of perfect rationality, an the various sorts of argument against them; (...) clarifies which conceptions of perfect rationality are targeted by which arguments; and finally attempts to systematize the results available to date. (shrink)

While game theory has been transformative for decision making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-k reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the quantal hierarchy model, which can relax both mutual consistency and best response while still approximating level-k, (...) QRE, or typical Nash equilibrium behavior in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the quantal hierarchy model in several canonical economic games, both simultaneous and sequential, using out-of-sample modelling. (shrink)

This article connects recent work in formal epistemology to work in economics and computer science. Analysing the Dutch Book Arguments, Epistemic Utility Theory and Objective Bayesian Epistemology we discover that formal epistemologists employ the same argument structure as economists and computer scientists. Since similar approaches often have similar problems and have shared solutions, opportunities for cross-fertilisation abound.

The rational expectations hypothesis holds that agents should be modeled as not making systematic forecasting errors and has become a central model-building principle of modern economics. The hypot...

The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme. The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this in terms (...) of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory.Keywords: Epistemic Programme; Game theory; Interactive epistemology; Mathematisation; Nash equilibrium. (shrink)

Do conventions need to be common knowledge in order to work? David Lewis builds this requirement into his definition of a convention. This paper explores the extent to which his approach finds support in the game theory literature. The knowledge formalism developed by Robert Aumann and others militates against Lewis’s approach, because it shows that it is almost impossible for something to become common knowledge in a large society. On the other hand, Ariel Rubinstein’s Email Game suggests that coordinated action (...) is no less hard for rational players without a common knowledge requirement. But an unnecessary simplifying assumption in the Email Game turns out to be doing all the work, and the current paper concludes that common knowledge is better excluded from a definition of the conventions that we use to regulate our daily lives. (shrink)

The notion of bounded rationality has recently gained considerable popularity in the behavioural and social sciences. This article surveys the different usages of the term, in particular the way ‘anomalosus’ behavioural phenomena are elicited, how these phenomena are incorporated in model building, and what sort of new theories of behaviour have been developed to account for bounded rationality in choice and in deliberation. It also discusses the normative relevance of bounded rationality, in particular as a justifier of non‐standard reasoning and (...) deliberation heuristics. For each of these usages, the overview discusses the central methodological problems. (shrink)

This article provides a critical examination of Ken Binmore’s theory of the social contract in light of philosophical discussions about moral naturalism and moral conventionalism. Binmore’s account builds on the popular philosophical device of the original position but gives it a naturalistic twist. I argue that this makes it vulnerable to moral skepticism. I explore a possible answer to the moral skeptic’s challenge, building on the fact that Binmore’s account displays a variant of moral conventionalism. I ultimately conclude however that (...) the conventionalist answer leads to a purely behaviorist view of morality, which implies that there is nothing special about morality and fairness norms. I propose alternative interpretations of conventionalism. These accounts escape most of the difficulties because they place emphasis on the reasons that establish a moral convention. (shrink)

This article argues that evolutionary models based on selection validate, under appropriate conditions, the relevance of optimality as an explanatory mechanism in rational choice theory. The reason is that these frameworks share the mechanism that drives the results, namely, optimization, even if they situate it at different levels. The consequences of our argument are twofold. First, it resolves the tension between those predictions of rational choice theory that are accurate and the evidence showing that individuals seldom optimize. Second, it relativizes (...) the explanatory import of rationality without diminishing the role of optimization as a mechanism. (shrink)

Robert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation (...) when a given node is reached can be thought of as the result of a joint act of learning (via public announcements) that the node is reached. We then use the notion of “stable belief”, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann’s and compatible with the implicit assumptions (the “epistemic openness of the future”) underlying Stalnaker’s criticism of Aumann’s proof. The “dynamic” nature of our concept of rationality explains why our condition avoids the apparent circularity of the “backward induction paradox”: it is consistent to (continue to) believe in a player’s rationality after updating with his irrationality. (shrink)

Equilibrium game theory borrows from neoclassical economics its rationality concept which it immediately puts to work in order to produce the basic results it needs for building an elaborate narrative of social interaction. This paper focuses on some recent objections to game theory's use of rationality assumptions in general, and of backward induction and subgame perfection in particular, and interprets them in the light of the postmodern critique of the grand meta-narratives which social theorists often rely on for social explanation. (...) The paper presents a defence of game theory which seeks to accommodate the postmodern critique. However, it goes on to show that such a defence is illegitimate and claims that the problem lies with the faulty conceptualisation of the main concept on which game theory rests: that of Reason. Having established the nature of the problem, it considers three alternative interpretations (Humean, postmodern and Hegelian) of why the problem resists logical solutions and of its significance for social theory. (shrink)

Two philosophical questions arise about rationality in centipede games that are logically prior to attempts to apply the formal tools of game theory to this topic. First, given that the players have common knowledge of mutual rationality and common knowledge that they are each motivated solely to maximize their own profits, is there a backwards-induction argument that employs only familiar non-technical concepts about rationality, leads to the conclusion that the first player is rationally obligated to end the game at the (...) first step, is deductively valid, employs premises all of which are prima facie highly plausible, and is prima facie sound and )? Second, if there is such an argument, then is it actually sound, or is it instead defective somehow despite being prima facie sound? Addressing these two questions is our project. We present a backwards-induction argument that is prima facie sound; we argue that it is an instance of the notorious sorites paradox, and hence that the concepts of rational obligatoriness and rational permissibility are vague; and we briefly address the potential consequences of all this for the foundations of game theory and decision theory. (shrink)

Although it may seem from its formalism that game theory must have sprung from the mind of John von Neumann as a corollary of his work on computers or theoretical physics, it should come as no real surprise to philosophers that game theory is the articulation of a historically developing philosophical conception of rationality in thought and action. The history of ideas about rationality is deeply contradictory at many turns. While there are theories of rationality that claim it is fundamentally (...) social and aims at understanding and molding all facets of human psychological life, game theory takes rationality to be essentially located in individuals and to concern only the means to achieve predetermined ends. Thus, there are some thinkers who have made important contributions to this history who do not appear in the story of game theory at all, among them, Plato, Kant, and Hegel. There is, however, a clear trail to follow linking theories of instrumental rationality from Aristotle to the nineteenth-century marginalist economists and ultimately to von Neumann and Morgenstern and contemporary game theorists, that historically grounds game theory as a model of rational interaction. (shrink)

The development of evolutionary game theory is closely linked with two interdisciplinary exchanges: the import of game theory into biology, and the import of biologists’ version of game theory into economics. This paper traces the history of these two import episodes. In each case the investigation covers what exactly was imported, what the motives for the import were, how the imported elements were put to use, and how they related to existing practices in the respective disciplines. Two conclusions emerged from (...) this study. First, concepts derived from the unity of science discussion or the unification accounts of explanation are too strong and too narrow to be useful for analysing these interdisciplinary exchanges. Secondly, biology and economics—at least in relation to EGT—show significant differences in modelling practices: biologists seek to link EGT models to concrete empirical situations, whereas economists pursue conceptual exploration and possible explanation.Keywords: Models; Evolutionary game theory; Interdisciplinarity; Unification; Unity of science; Theory import; Biology; Economics. (shrink)

We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common (...) reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction. (shrink)

Subjunctive conditionals are fundamental to rational decision both in single agent and multiple agent decision problems. They need explicit analysis only when they cause problems, as they do in recent discussions of rationality in extensive form games. This paper examines subjunctive conditionals in the theory of games using a strict revealed preference interpretation of utility. Two very different models of games are investigated, the classical model and the limits of reality model. In the classical model the logic of backward induction (...) is valid, but it does not use subjunctive conditionals; the relevant subjunctive conditionals do not even make sense. In the limits of reality model the subjunctive conditionals do make sense but backward induction is valid only under special assumptions. (shrink)

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an (...) equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

Conceptualizing behavior decision theoretically as being ‘pulled’ (by an expected future) is fundamentally different from conceptualizing it as ‘pushed’ (or determined by past conditions according to causal laws). However, the fundamental distinction between teleological and non-teleological explanations not withstanding, decision-theoretic and evolutionary ‘ways of world making’ lead to strikingly similar forms of political, philosophical, and economic models. Common Hobbesian roots can account historically for the emergence of such a common ‘PPE’ outlook, while a game-theoretic framework of indirect evolution can accommodate (...) the fundamental methodological tension between teleological and non-teleological approaches or the ‘humanities’ and the ‘science’ traditions in PPE’s disciplines. (shrink)

We present a new class of models of players’ reasoning in non-cooperative games, inspired by David Lewis's account of common knowledge. We argue that the models in this class formalize common knowledge of rationality in a way that is distinctive, in virtue of modelling steps of reasoning; and attractive, in virtue of being able to represent coherently common knowledge of any consistent standard of individual decision-theoretic rationality. We contrast our approach with that of Robert Aumann, arguing that the former avoids (...) and diagnoses certain paradoxes to which the latter may give rise when extended in particular ways. (shrink)

IntroductionA quick glance at the opening paragraphs in many of the classic logic textbooks reveals a common view: Logical methods highlight the reasoning patterns of a single agent engaged in some form of mathematical thinking.A sampling from my bookshelf: Shoenfield’s Mathematical Logic: “Logic is the study of reasoning; and mathematical logic is the study of the type of reasoning done by mathematicians”; Enderton’s A Mathematical Introduction of Logic: “Symbolic logic is a mathematical model of deductive thought”; and Chiswell and Hodges (...) Mathematical Logic: “In this course we shall study some ways of proving statements.” However, this traditional view of the “subject matter” of logic is expanding. There is a growing literature using phrases such as “rational interaction” or “information flow” to describe its subject matter while still employing traditional logical methods. The clearest example of this can be found in the work of Johan van Benthem and others on l .. (shrink)

Logic is breaking out of the confines of the single-agent static paradigm that has been implicit in all formal systems until recent times. We sketch some recent developments that take logic as an account of information-driven interaction. These two features, the dynamic and the social, throw fresh light on many issues within logic and its connections with other areas, such as epistemology and game theory.

Some practical criteria for free-will are suggested where free-will is a matter of degree. It is argued that these are more appropriate than some extremely idealised conceptions. Thus although the paper takes lessons from philosophy it avoids idealistic approaches as irrelevant. A mechanism for allowing an agent to meet these criteria is suggested: that of facilitating the gradual emergence of free-will in the brain via an internal evolutionary process. This meets the requirement that not only must the choice of action (...) be free but also choice in the method of choice, and choice in the method of choice of the method of choice etc. This is directly analogous to the emergence of life from non-life. Such an emergence of indeterminism with respect to the conditions of the agent fits well with the `Machiavellian Intelligence Hypothesis' which posits that our intelligence evolved (at least partially) to enable us to deal with social complexity and modelling `arms races'. There is a clear evolutionary advantage in being internally coherent in seeking to fulfil ones goals and unpredictable by ones peers. To fully achieve this vision several other aspects of cognition are necessary: open-ended strategy development; the meta-evolution of the evolutionary process; the facility to anticipate the results of strategies; and the situating of this process in a society of competitive peers. Finally the requirement that reports of the deliberations that lead to actions need to be socially acceptable leads to the suggestion that the language that the strategies are developed within be subject to a normative process in parallel with the development of free-will. An appendix outlines a philosophical position in support of my position. (shrink)

This paper suggests that Nash equilibrium can be interpreted as a conceptual tool for addressing comparative-statics issues on an aggregate level. Together with additional assumptions, Nash equilibrium helps generate testable predictions about changes or differences of behavior induced by changes or differences of exogenous variables. However, Nash-equilibrium behavior, as such, is not subject to empirical testing. Instead, widespread and persistent behavior is modeled as a Nash equilibrium by assumption. The paper argues that this interpretation is in line with the traditional (...) use of an equilibrium concept in price theory. The suggested interpretation is illustrated with the model of public-goods provision. The paper compares this interpretation of Nash equilibrium with other interpretations and discusses its limits. (shrink)

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on plausibility models. Similarly to other epistemic statements, dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we "simulate" the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought of as (...) the result of a joint act of learning that the node is reached. We then use the notion of "stable belief, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann's and compatible with the implicit assumptions underlying Stalnaker's criticism of Aumann's proof. The "dynamic" nature of our concept of rationality explains why our condition avoids the apparent circularity of the "backward induction paradox": it is consistent to believe in a player's rationality after updating with his irrationality. (shrink)

Although it may seem from its formalism that game theory must have sprung from the mind of John von Neumann as a corollary of his work on computers or theoretical physics, it should come as no real surprise to philosophers that game theory is the articulation of a historically developing philosophical conception of rationality in thought and action. The history of ideas about rationality is deeply contradictory at many turns. While there are theories of rationality that claim it is fundamentally (...) social and aims at understanding and molding all facets of human psychological life, game theory takes rationality to be essentially located in individuals and to concern only the means to achieve predetermined ends. Thus, there are some thinkers who have made important contributions to this history who do not appear in the story of game theory at all, among them, Plato, Kant, and Hegel. There is, however, a clear trail to follow linking theories of instrumental rationality from Aristotle to the nineteenth-century marginalist economists and ultimately to von Neumann and Morgenstern and contemporary game theorists, that historically grounds game theory as a model of rational interaction. (shrink)

For the past 20 years or so the literature on noncooperative games has been centered on the search for an equilibrium concept that expresses the notion of rational behavior in interactive situations. A basic tenet in this literature is that if a “rational solution” exists, it must be a Nash equilibrium. The consensus view, however, is that not all Nash equilibria can be accepted as rational solutions. Consider, for example, the game of Figure 1.