Game theory is the systematic study of interdependent rational choice. It should be distinguished from decision theory, the systematic study of individual (practical and epistemic) choice in parametric contexts (i.e., where the agent is choosing or deliberating independently of other agents). Decision theory has several applications to ethics (see Dreier 2004; Mele and Rawlings 2004). Game theory may be used to explain, to predict, and to evaluate human behavior in contexts where the outcome of action depends on what several agents (...) choose to do and where their choices depend on what others choose to do. (See the entry on game theory) Game theory consequently is relevant to ethics, and it is used in moral and political philosophy in a variety of ways. We shall concentrate on the influence and use of game theory in ethics and those parts of political theory involving norms or principles of justice, ignoring questions about political and legal institutions on the one hand and questions about issues dealing with moral virtues on the other. (shrink)

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry (...) it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

Les notions logiques de conséquence sont fréquemment reliées à des concepts de solution de la théorie des jeux. Dans ce contexte domine la correspondance entre une formule classiquement valide et l’existence d’une stratégie gagnante pour un joueur dans un jeu à deux joueurs. Nous proposons une extension conservative de la notion classique de conséquence basée sur une généralisation du concept de solution de jeu d’équilibre de Nash.

Les notions logiques de conséquence sont fréquemment reliées à des concepts de solution de la théorie des jeux. Dans ce contexte domine la correspondance entre une formule classiquement valide et l’existence d’une stratégie gagnante pour un joueur dans un jeu à deux joueurs. Nous proposons une extension conservative de la notion classique de conséquence basée sur une généralisation du concept de solution de jeu d’équilibre de Nash.

The problem of knowledge.--The acquisition of knowledge.--The assimilation of knowledge.--The deployment of knowledge.--Knowing, doing and being.--Absent objects.--The mind-body problem.--The knowledge of the known.--The subjectivity of a realist.--Activity as a source of knowledge.--On beliefs and believing.--Adaptive responses and the ecosystem.--The reality game.

Kin selection, reciprocity and group selection are widely regarded as evolutionary mechanisms capable of sustaining altruism among humans andother cooperative species. Our research indicates, however, that these mechanisms are only particular examples of a broader set of evolutionary possibilities.In this paper we present the results of a series of simple replicator simulations, run on variations of the 2–player prisoner's dilemma, designed to illustrate the wide range of scenarios under which altruism proves to be robust under evolutionary pressures. The set of (...) mechanisms we explore is divided into four categories :correlation, group selection, imitation, and punishment. We argue that correlation is the core phenomenon at work in all four categories. (shrink)

There are two general classes of social conventions: conventions of coordination, and conventions of partial conflict. In coordination problems, the interests of the agents coincide, while in partial conflict problems, some agents stand to gain only if other agents unilaterally make certain sacrifices. Lewis' (1969) pathbreaking analysis of convention in terms of game theory focuses on coordination problems, and cannot accommodate partial conflict problems. In this paper, I propose a new game-theoretic definition of convention which generalizes previous game-theoretic definitions (Lewis (...) 1969, Vanderschraaf 1995), and which can be used to characterize norms of justice in partial conflict situations. I argue that the key structural property necessary for a social arrangement to be a convention is that it be conditionally self-enforcing, in the sense that: (i) each agent has a decisive reason to follow her end of the arrangement given that she expects all to do likewise, (ii) given a different set of expectations, some agents would have had a decisive reason to deviate, and (iii) these facts are common knowledge. This leads to a definition of convention as a strict correlated equilibrium (Aumann 1974) together with appropriate common knowledge conditions. Examples are given in which it is shown how this more general account of convention can be used to analyze norms of justice as well as coordination problems. It is only a general sense of common interest; which sense all the members of the society express to one another, and which induces them to regulate their conduct by certain rules. I observe, that it will be for my interest to leave another in the possession of his goods, provided he will act in the same manner with regard to me. He is sensible of a like interest in the regulation of his conduct. When this common sense of interest is mutually express'd, and is known to both, it produces a suitable resolution and behavior. And this may properly be call'd a convention or agreement betwixt us,.. (shrink)

In recent years, a number of authors have used gametheoretic reasoning to explain why purely self-interested agentswould ever conform their economic activities with the requirements of justice, when by doing so they forego opportunities to reapunilateral net gains by exploiting others. In this paper, I argue that Hume's justification of honest economic exchanges between self-interested agents in the Treatise foreshadows this contemporary literature. Hume analyzes the problem of explaining justice in self-interested economic exchange as a problem of agents coordinating on (...) a pattern of reciprocal cooperation, as opposed to some other behavioral pattern such as reciprocal exploitation, in exchanges repeated over time. Hume's arguments anticipate informally thecontemporary interpretation of just economic practices as forming part of an equilibrium of a repeated game. I close the paper by arguing that Hume does not provide a satisfactory explanation of how the mutual expectations that support justice in economic exchange arise in a community of self-interested agents. The problem Hume leaves unsolved is one of equilibrium selection, that is: Why do agents follow an equilibrium corresponding to just economic exchanges rather than some other equilibrium corresponding to unjust exchanges? I also argue that contemporary game theory still lacks a satisfactory theory of equilibrium selection, but that such a theory would lead us closer to a satisfactory Humean reconciliation of justice and self-interest in economic exchange. (shrink)

Aconvention is a state in which agents coordinate their activity, not as the result of an explicit agreement, but because their expectations are aligned so that each individual believes that all will act so as to achieve coordination for mutual benefit. Since agents are said to follow a convention if they coordinate without explicit agreement, the notion raises fundamental questions: (1) Why do certain conventions remain stable over time?, and (2) How does a convention emerge in the first place? In (...) a pioneering study, Lewis (1969) addresses these questions by applyingnoncooperative game theory. Lewis defines a convention as aNash coordination equilibrium of a noncooperative game that issalient, that is, it is somehow conspicuous to the agents so that all expect one another to conform with the equilibrium. This paper presents a new game theoretic definition of conventions, which formalizes the notion of salience and which also generalizes the class of conventions Lewis discusses in his work. I define a convention as acorrelated equilibrium (Aumann 1974, 1987) satisfying apublic intentions criterion: Every agent wants his intended action to becommon knowledge. I argue that many conventions correspond to correlated equilibria that are not Nash equilibria, and that this is consistent with Lewis' general viewpoint. Finally, I argue that game theoretic characterizations of convention, such as Lewis' and my own, help to explain a convention's stability, but that a fully satisfactory account of the emergence of convention requires a theory of equilibrium selection beyond the scope of Lewis' work. (shrink)

1. One of the main aims of this paper is to study the possibilities for free-riding type of behavior in various kinds of many-person interaction situations. In particular it will be of interest to see what kinds of game-theoretic structures, defined in terms of the participants' outcome-preferences, can be involved in cases of free-riding. I shall also be interested in the related problem or dilemma of collective action in a somewhat broader sense. By the dilemma of collective action I mean, (...) generally speaking, the conflict between individual and collective rationality and the conflict between corresponding actions, in the sense it has been discussed in recent literature. Typically (although not invariably) collective action problems and free-rider problems coexist. Let me start my discussion by considering what Elster (1985) has to say about the subject. First, the notion of collective action itself should be characterized. Elster defines it as follows (p. 137): "By collective action I mean the choice by all or most individuals of the course of action that, when chosen by all or most individuals, leads to the collectively best outcome." While this characterization is informative in the present context, I think that it is not appropriate as a general characterization. It may provide a sufficient condition, but it fails as a necessary condition. One reason for this is that there may not be a single collectively best outcome at all. Instead, I suggest we follow common sense and take collective action simply to be action by a collection or group of people, where these people (or at least many of them) act with the aim of achieving a common end or goal (this notion understood very broadly so as to include e.g. following norms, practices, and customs). We also require of a situation of collective action that the participants have several (or at least two) possible courses of action open to them. Elster's above definition of collective action goes in terms of the collectively best outcome or goal. (shrink)

Edna Ullmann-Margalit provides an original account of the emergence of norms. Her main thesis is that certain types of norms are possible solutions to problems posed by certain types of social interaction situations. She presents illuminating discussions of Prisoners' Dilemma, co-ordination, and inequality situations.

This paper proposes a game-theoretic solution of the surprise examination problem. It is argued that the game of “matching pennies” provides a useful model for the interaction of a teacher who wants her exam to be surprising and students who want to avoid being surprised. A distinction is drawn between prudential and evidential versions of the problem. In both, the teacher should not assign a probability of zero to giving the exam on the last day. This representation of the problem (...) provides a diagnosis of where the backwards induction argument, which “proves” that no surprise exam is possible, is mistaken. (shrink)

even if an equilibrium is asymptotically stable, that is no guarantee that the system will reach that equilibrium unless we know that the system's initial state is sufficiently close to the equilibrium. Global stability of an equilibrium, when we have it, gives the equilibrium a much more powerful explanatory role. An equilibrium is globally asymptotically stable if the dynamics carries every possible initial state in the interior of the state space to that equilibrium. If an equilibrium is globally stable, it (...) can have.. (shrink)

If it was a matter of hunting a deer, everyone well realized that he must remain faithful to his post; but if a hare happened to pass within reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple..." Rousseau's story of the hunt leaves many questions open. What are the values of a hare and of an individual's share of the deer given a successful hunt? What is the probability that (...) the hunt will be successful if all participants remain faithful to the hunt? Might two deer hunters decide to chase the hare? (shrink)

In this paper we study language use and language organisation by making use of Lewisean signalling games. Standard game theoretical approaches are contrasted with evolutionary ones to analyze conventional meaning and conversational interpretation strategies. It is argued that analyzing successful communication in terms of standard game theory requires agents to be very rational and fully informed. The main goal of the paper is to show that in terms of evolutionary game theory we can motivate the emergence and self-sustaining force of (...) (i) conventional meaning and (ii) some conversational interpretation strategies in terms of weaker and, perhaps, more plausible assumptions. (shrink)

This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies are critically (...) surveyed. Inthe second part, the doctrine of games as explanations for logic isassessed, and the relevance of a conceptual analysis of games tocognition discussed. It is suggested that the notion of evolution playsa part in the game-theoretic concept of meaning. (shrink)

The paradoxical view of warnock and hodgson that act-Utilitarianism must have disutility is criticised. Simple examples in game theory style show that it does not defeat the possibility of cooperation and that it allows an approximation to truth-Telling. Promising would indeed have only a limited role in an act-Utilitarian society, But that is because its normal function is to aid compromise between divergent purposes. Also, The efforts of a single act-Utilitarian in a non-Act-Utilitarian society need not frustrate themselves, If he (...) is not too candid. (shrink)

Arising out of the author's lifetime fascination with the links between the formal language of mathematical models and natural language, this short book comprises five essays investigating both the economics of language and the language of economics. Ariel Rubinstein touches the structure imposed on binary relations in daily language, the evolutionary development of the meaning of words, game-theoretical considerations of pragmatics, the language of economic agents and the rhetoric of game theory. These short essays are full of challenging ideas for (...) social scientists that should help to encourage a fundamental rethinking of many of the underlying assumptions in economic theory and game theory. As a postscript two economists, Tilman Borgers and Bart Lipman, and a logician, Johan van Benthem offer comments. (shrink)

_ Convention_ was immediately recognized as a major contribution to the subject and its significance has remained undiminished since its first publication in 1969. Lewis analyzes social conventions as regularities in the resolution of recurring coordination problems-situations characterized by interdependent decision processes in which common interests are at stake. Conventions are contrasted with other kinds of regularity, and conventions governing systems of communication are given special attention.

In 1792 Wilhelm von Humboldt wrote his treatise Ideen zu einem Versuch, die Gränzen der Wirksamkeit des Staates zu bestimmen . The treatise supports a notion of the state one would nowadays call libertarian. Seen against the backdrop of his time, characterized by far-reaching governmental regulations, Humboldt’s work must be considered a radical manifesto of deregulation.1 Analyzing various fields of potential governmental activity, Humboldt pleaded in favor of a minimum of governmental intervention.

The paper first summarizes the author's decision-theoretical model of moral behavior, in order to compare the moral implications of the act-utilitarian and of the rule-utilitarian versions of utilitarian theory. This model is then applied to three voting examples. It is argued that the moral behavior of act-utilitarian individuals will have the nature of a noncooperative game, played in the extensive mode, and involving action-by-action maximization of social utility by each player. In contrast, the moral behavior of rule-utilitarian individuals will have (...) the nature of a cooperative game, played in the normal mode, and involving a firm commitment by each player to a specific moral strategy (viz. to the strategy selected by the rule-utilitarian choice criterion) — even if some individual actions prescribed by this strategy, when considered in isolation, should fail to maximize social utility. The most important advantage that rule utilitarianism as an ethical theory has over act utilitarianism lies in its ability to give full recognition to the moral and social importance of individual rights and personal obligations. It is easy to verify that action-by-action maximization of social utility, as required by act utilitarianism, would destroy these rights and obligations. In contrast, rule utilitarianism can fully recognize the moral validity of these rights and obligations precisely because of its commitment to an overall moral strategy, independent of action-by-action social-utility maximization. The paper ends with a discussion of the voter's paradox problem. The conventional theory of rational behavior cannot avoid the paradoxical conclusion that, in any large electorate, voting is always an irrational activity because one's own individual vote is extremely unlikely to make any difference to the outcome of any election. But it can be shown that, by using the principles of rule-utilitarian theory, this paradox can easily be resolved and that, in actual fact, voting, even in large electorates, may be perfectly rational action. More generally, the example of rule utilitarianism shows what an important role the concept of a rational commitment can play in the analysis of rational behavior. (shrink)

Is morality rational? In this book Gauthier argues that moral principles are principles of rational choice. He proposes a principle whereby choice is made on an agreed basis of cooperation, rather than according to what would give an individual the greatest expectation of value. He shows that such a principle not only ensures mutual benefit and fairness, thus satisfying the standards of morality, but also that each person may actually expect greater utility by adhering to morality, even though the choice (...) did not have that end primarily in view. In resolving what may appear to be a paradox, the author establishes morals on the firm foundation of reason. Gauthier's argument includes an account of value, linking it to preference and utility; a discussion of the curcumstances in which morality is unnecessary; and an application of morals by agreement to relations between peoples at different levels of development and different generations. Finally, he reflects on the assumptions about individuality and community made by his account of rationality and morality. (shrink)

Gauthier's argument for constrained maximization, presented inMorals by Agreement, is perfected by taking into account the possibility of accidental exploitation and discussing the limitations on the values of the parameters which measure the translucency of the actors. Gauthier's argument is nevertheless shown to be defective concerning the rationality of constrained maximization as a strategic choice. It can be argued that it applies only to a single actor entering a population of individuals who are themselves not rational actors but simple rule-followers. (...) A proper analysis of the strategic choice situation involving two rational actors who confront each other shows that constrained maximization as the choice of both actors can only result under very demanding assumptions. (shrink)

Brian Skyrms has argued that the evolution of the social contract may be explained using the tools of evolutionary game theory. I show in the first half of this paper that the evolutionary game-theoretic models are often highly sensitive to the specific processes that they are intended to simulate. This sensitivity represents an important robustness failure that complicates Skyrms's project. But I go on to make the positive proposal that we may none the less obtain robust results by simulating the (...) population structures that existed among our evolutionary ancestors. It is by extending the evolutionary models in this way that we should pursue the project of explaining the evolution of the social contract. (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)

Game theoretic explanations of the evolution of human behavior have become increasingly widespread. At their best, they allow us to abstract from misleading particulars in order to better recognize and appreciate broad patterns in the phenomena of human social life. We discuss this explanatory strategy, contrasting it with the particularist methodology of contemporary evolutionary psychology. We introduce some guidelines for the assessment of evolutionary game theoretic explanations of human behavior: such explanations should be representative, robust, and flexible. Distinguishing these features (...) sharply can help to clarify the import and accuracy of game theorists' claims about the robustness and stability of their explanatory schemes. Our central example is the work of Brian Skyrms, who offers a game theoretic account of the evolution of our sense of justice. Modeling the same Nash game as Skyrms, we show that, while Skyrms' account is robust with respect to certain kinds of variation, it fares less well in other respects. (shrink)

Edna Ullmann-Margalit provides an original account of the emergence of norms. Her main thesis is that certain types of norms are possible solutions to problems posed by certain types of social interaction situations. She presents illuminating discussions of Prisoners' Dilemma, co-ordination, and inequality situations.

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)

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal analogy (...) between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation. (shrink)

The purpose of this paper is to work toward an explicit logic and semantics for a game theoretically inspired theory of action. The purpose of the logic is to explicate the conceptual machinery implicit in the dialogue-game model of rational discourse developed in Carlson (1983).A variety of ideas and techniques of modal and philosophical logic are used to define a model structure that generalizes the game theoretical notion of a game in extensive form (von Neumann and Morgenstern, 1944). Relative to (...) this model structure, semantic characterizations are given to the action-theoretic notions oftime, possibility, belief, preference, ability, intention, action, andrationality. The unification of these characterizations under the game-theoretical paradigm leads to insights about the logical interdependences between these concepts. (shrink)