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 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)

The 'Evolution of Cooperation' addresses a simple yet age-old question; If living things evolve through competition, how can cooperation ever emerge? Despite the abundant evidence of cooperation all around us, there existed no purely naturalistic answer to this question until 1979, when Robert Axelrod famously ran a computer tournament featuring a standard game-theory exercise called The Prisoner's Dilemma. To everyone's surprise, the program that won the tournament, named Tit for Tat, was not only the simplest but the most "cooperative" entrant. (...) This unexpected victory proved that cooperation - one might even say altruism - is mathematically possible and therefore needs no hidden hand or divine agent to create and sustain it. A great roadblock to the understanding of all sorts of behavior was at last removed. The updated edition includes an extensive new chapter on cooperation in cancer cells and among terrorist organizations. (shrink)

The scientist's decision of accepting a given proposition is assumed to be dependent on two factors: the scientist's 'private' information about the value of that statement and the proportion of colleagues who also accept it. This interdependence is modelled in an economic fashion, and it is shown that it may lead to multiple equilibria. The main conclusions are that the evolution of scientific knowledge can be path, dependent, that scientific revolutions can be due to very small changes in the empirical (...) evidence, and that not all possible equilibria are necessarily efficient, neither in the economic nor in the epistemic sense. These inefficiencies, however, can be eliminated if scientists can form coalitions. (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)

We discuss games of both perfect and imperfect information at two levels of structural detail: players’ local actions, and their global powers for determining outcomes of the game. We propose matching logical languages for both. In particular, at the ‘action level’, imperfect information games naturally model a combined ‘dynamic-epistemic language’ – and we find correspondences between special axioms and particular modes of playing games with their information dynamics. At the ‘outcome level’, we present suitable notions of game equivalence, plus some (...) simple representation results. (shrink)

In the Divide-the-Dollar (DD) game, two players simultaneously make demands to divide a dollar. Each player receives his demand if the sum of the demands does not exceed one, a payoff of zero otherwise. Note that, in the latter case, both parties are punished severely. A major setback of DD is that each division of the dollar is a Nash equilibrium outcome. Observe that, when the sum of the two demands x and y exceeds one, it is as if Player (...) 1's demand x (or his offer (1−x) to Player 2) suggests that Player 2 agrees to λx < 1 times his demand y so that Player 1's demand and Player 2's modified demand add up to exactly one; similarly, Player 2's demand y (or his offer (1−y) to Player 1) suggests that Player 1 agrees to λyx so that λyx+y = 1. Considering this fact, we change DD's payoff assignment rule when the sum of the demands exceeds one; here in this case, each player's payoff becomes his demand times his λ; i.e., each player has to make the sacrifice that he asks his opponent to make. We show that this modified version of DD has an iterated strict dominant strategy equilibrium in which each player makes the egalitarian demand 1/2. We also provide a natural N-person generalization of this procedure. (shrink)

This paper provides an overview of developments in the application of game theory to moral philosophy. Game theory has been used in moral theory in three ways. First, as a tool to analyze the function of moral norms. Secondly, to characterize bargaining about moral norms. Thirdly, the paper demonstrates how game theory can make sense of the authority of moral norms in a way that renders the concept suitable for further analysis.

This article argues that various deviations from the basic principles of the scientific ethos – primarily the appearance of pseudoscience in scientific communities – can be formulated and explained using specific models of game theory, such as the prisoner’s dilemma and the iterated prisoner’s dilemma. The article indirectly tackles the deontology of scientific work as well, in which it is assumed that there is no room for moral skepticism, let alone moral anti-realism, in the ethics of scientific communities. Namely, on (...) the basis of the generally accepted dictum of scientific endeavor as the pursuit of knowledge exclusively for knowledge’s sake, scientifically »right« behavior is seen to be clearly defined and distinguishable from scientifically »wrong« behavior. After elucidating the basic principles of game theory, the article illustrates – by using imaginary and real cases, as well as some views from the philosophyof biology (the units of selection debate) – how this sort of reasoning could be applied in an analysis of the functioning of science. (shrink)

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.

Martin Kusch puts forth two controversial ideas: that knowledge is a social status and that knowledge is primarily the possession of groups rather than individuals. He defends the radical implications of his views: that knowledge is political, and that it varies with communities. This bold approach to epistemology is a challenge to philosophy and the wider academic world.

The law persists because people have reasons to comply with its rules. What characterizes those reasons is their interdependence: each of us only has a reason to comply because he or she expects the others to comply for the same reasons. The rules may help us to solve coordination problems, but the interaction patterns regulated by them also include Prisoner's Dilemma games, Division problems and Assurance problems. In these "games" the rules can only persist if people can be expected to (...) be moved by considerations of fidelity and fairness, not only of prudence.This book takes a fresh look at the perennial problems of legal philosophy - the source of obligation to obey the law, the nature of authority, the relationship between law and morality, and the nature of legal argument - from the perspective of this conventionalist understanding of social rules. It argues that, since the resilience of such rules depends on cooperative dispositions, conventionalism, properly understood, does not imply positivism. (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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

Most traditional epistemologists see trust and knowledge as deeply antithetical: we cannot know by trusting in the opinions of others; knowledge must be based on evidence, not mere trust. I argue that this is badly mistaken. Modern knowers cannot be independent and self-reliant. In most disciplines, those who do not trust cannot know. Trust is thus often more epistemically basic than empirical evidence or logical argument, for the evidence and the argument are available only through trust. Finally, since the reliability (...) of testimonial evidence depends on the trustworthiness of the testifier, this implies that knowledge often rests on a foundation of ethics. The rationality of many of our beliefs depends not only on our own character, but on the character of others. (shrink)

find myself believing all sorts 0f things for which I d0 not possess evidence: that smoking cigarettes causes lung cancer, that my car keeps stalling because the carburetor needs LO be rebuilt, that mass media threaten democracy, that slums cause emotional disorders, that my irregular heart beat is premature ventricular contraction, that students} grades are not correlated with success in the ncmacadcmic world, that nuclear power plants are not safe (enough) . . . The list 0f things I believe, though (...) I have no evidence for the truth of them, is, if not infinite, virtually endless. And.. (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)

Evolutionary game theoretic accounts of justice attempt to explain our willingness to follow certain principles of justice by appealing to robustness properties possessed by those principles. Skyrms (1996) offers one sketch of how such an account might go for divide-the-dollar, the simplest version of the Nash bargaining game, using the replicator dynamics of Taylor and Jonker (1978). In a recent article, D'Arms et al. (1998) criticize his account and describe a model which, they allege, undermines his theory. I sketch a (...) theory of evolutionary explanations of justice which avoids their methodological criticisms, and develop a spatial model of divide-the-dollar with more robust convergence properties than the models of Skyrms (1996) and D'Arms et al. (1998). (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)

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)

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)

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)