Provides the reader who has not studied game theory a brief and non‐technical introduction to the main categories of models and forms of analysis: strategic‐ form games; extensive‐form games; dominance; and Nash equilibrium.

Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality (...) but also common knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological game theory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; game theory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (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)

_A new theory of how and why we cooperate, drawing from economics, political theory, and philosophy to challenge the conventional wisdom of game theory_ Game theory explains competitive behavior by working from the premise that people are self-interested. People don’t just compete, however; they also cooperate. John Roemer argues that attempts by orthodox game theorists to account for cooperation leave much to be desired. Unlike competing players, cooperating players take those actions that they would (...) like others to take—which Roemer calls “Kantian optimization.” Through rigorous reasoning and modeling, Roemer demonstrates a simpler theory of cooperative behavior than the standard model provides. (shrink)

Is capitalism inherently predatory? Must there be winners and losers? Is public interest outdated and free-riding rational? Is consumer choice the same as self-determination? Must bargainers abandon the no-harm principle? Prisoners of Reason recalls that classical liberal capitalism exalted the no-harm principle. Although imperfect and exclusionary, modern liberalism recognized individual human dignity alongside individuals' responsibility to respect others. Neoliberalism, by contrast, views life as ceaseless struggle. Agents vie for scarce resources in antagonistic competition in which every individual seeks dominance. This (...) political theory is codified in non-cooperative game theory; the neoliberal citizen and consumer is the strategic rational actor. Rational choice justifies ends irrespective of means. Money becomes the medium of all value. Solidarity and good will are invalidated. Relationships are conducted on a quid pro quo basis. However, agents can freely opt out of this cynical race to the bottom by embracing a more expansive range of coherent action. (shrink)

I explore a connection between Robert Nozick's account of decision value/symbolic utility in The Nature of Rationality and F. P. Ramsey's discussion of ethically neutral propositions in his 1926 essay , a discussion that Brian Skyrms in Choice and Chance credits with disclosing deeper foundations for expected utility than the celebrated Theory of Games and Economic Behavior of von Neumann and Morgenstern. Ramsey's recognition of ethically non-neutral propositions is essential to his foundational work, and the similarity of these propositions (...) to symbolic utility helps make the case that the latter belongs to the apparatus that constructs expected utility, rather than being reducible to it or being part of a proposal that can be cheerfully ignored. I conclude that decision value replaces expected utility as the central idea in (normative) decision theory. Expected utility becomes an approximation that is good enough when symbolic utility is not at stake. (shrink)

Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of (...) game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed. (shrink)

Groups of people perform acts that are subject to standards of rationality. A committee may sensibly award fellowships, or may irrationally award them in violation of its own policies. A theory of collective rationality defines collective acts that are evaluable for rationality and formulates principles for their evaluation. This book argues that a group's act is evaluable for rationality if it is the products of acts its members fully control. It also argues that such an act is collectively rational (...) if the acts of the group's members are rational. Efficiency is a goal of collective rationality, but not a requirement, except in cases where conditions are ideal for joint action and agents have rationally prepared for joint action.The people engaged in a game of strategy form a group, and the combination of their acts yields a collective act. If their collective act is rational, it constitutes a solution to their game. A theory of collective rationality yields principles concerning solutions to games. One principle requires that a solution constitute an equilibrium among the incentives of the agents in the game. In a cooperative game some agents are coalitions of individuals, and it may be impossible for all agents to pursue all incentives. Because rationality is attainable, the appropriate equilibrium standard for cooperative games requires that agents pursue only incentives that provide sufficient reasons to act. The book's theory of collective rationality supports an attainable equilibrium-standard for solutions to cooperative games and shows that its realization follows from individuals' rational acts.By extending the theory of rationality to groups, this book reveals the characteristics that make an act evaluable for rationality and the way rationality's evaluation of an act responds to the type of control its agent exercises over the act. The book's theory of collective rationality contributes to philosophical projects such as contractarian ethics and to practical projects such as the design of social institutions. (shrink)

Ender's tortured conscience is an illustration of the moral importance of following principles of just war theory—the “unspoken rules of manly warfare”—and their apparent tension with the demands of war and survival. This chapter talks about the ethics of conflict in Ender's various games—his battles and wars. It asks, was justice served in the Third Invasion and destruction of the bugger worlds, the event that came to be called the xenocide. Ender's life is actually a testimony to the just (...) war axiom that all people desire peace. In the tradition of just war theory, there are five principles that lay out the requirements of jus ad bellum, or how to go to war in an ethical way. They include just cause, legitimate authority, right intention, probability of success, and last resort. Ender's strategy is always to use devastating force to incapacitate the enemy. (shrink)

This is a two-volume set that provides an introduction to non-cooperative Game Theory. Volume 1 covers the basic concepts, while Volume 2 is devoted to advanced topics. The book is richly illustrated with approximately 400 figures. It is suitable for both self-study and as the basis for an undergraduate course in game theory as well as a first-year graduate-level class. It is written to be accessible to anybody with high-school level knowledge of mathematics. At the (...) end of each chapter there is a collection of exercises accompanied by detailed answers. The book contains approximately 180 exercises. (shrink)

Game theorists tend to model climate negotiations as a so-called ‘tragedy of the commons’. This is rather worrisome, since the conditions under which such commons problems have historically been solved are almost entirely absent in the case of international greenhouse gas emissions. In this paper, I will argue that the predictive accuracy of the tragedy model might not stem from the model’s inherent match with reality but rather from the model’s ability to make self-fulfilling predictions. I then sketch some (...) possible ways to dispel the tragedy, including (1) recognizing some ways the assumptions of the model fail, (2) taking seriously recent work suggesting that increasing greenhouse gas emissions is not in most nations’ own self-interest, and (3) preferring alternative models like collective risk dilemmas, bargaining games, or cooperative models. (shrink)

We consider a class of games, which we call “groups’ games”, in which players are partitioned into classes within which players may be considered indistinguishable. We compute explicit formulas for some of the principal values restricted to these games. This is particularly useful for dealing with games with a large number of players where the usual formulas would be impractical to compute. We give several examples that illustrate how this idea may be applied to concrete situations.

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)

We introduce a solution concept for cooperative games with transferable utility and a coalition structure that is proportional for two-player games. Our value is obtained from generalizing a proportional value for cooperative games with transferable utility in a way that parallels the extension of the Shapley value to the Owen value. We provide two characterizations of our solution concept, one that employs a property that can be seen as the proportional analog to Myerson’s balanced contribution property; and a (...) second one that relies on a consistency property. (shrink)

This article presents two theorems: a generalization of Löb’s Theorem that applies to formal proof systems operating with bounded computational resources, such as formal verification software or theorem provers, and a theorem on the robust cooperation of agents that employ proofs about one another’s source code as unexploitable criteria for cooperation. The latter illustrates a capacity for outperforming classical Nash equilibria and correlated equilibria, attaining mutually cooperative program equilibrium in the Prisoner’s Dilemma while remaining unexploitable, i.e., sometimes achieving the (...) outcome, and never receiving the outcome as player 1. (shrink)

During a cultural festival, artists and theaters act as a cartel by agreeing on pricing decisions that maximize the groups’ profit as a whole. We model the problem of sharing the profit created by a festival among organizing theaters as a cooperative game. In such a game, the worth of a coalition is defined as the theaters’ profit from the optimal fixation of prices. We show that this class of games is convex and we axiomatically characterize the (...) Shapley value for this class of games. We also provide an axiomatic basis for the downstream incremental solution. Finally, we apply this model to the NEXT festival, for which we have collected data. We propose an approach to derive the games’ vector from the data and we compute the different solutions. (shrink)

Fundamental aspects of human use of the environment can be explained by game theory. Game theory explains aggregate behaviour of the human species driven by perceived costs and benefits. In the ‘game’ of global environmental protection and conservation, the stakes are the living conditions of all species including the human race, and the playing field is our planet. The question is can we control humanity's hitherto endless appetite for resources before we irreparably harm the global (...) ecosystem and cause extinction of even more species? The central problem is that some proportion of the individuals or groups will behave selfishly. The inducement for using more than a fair share, or ‘cheating’, increases as that resource becomes rarer, thus the benefits of cheating increase. In addition, the total number of people is increasing, so the proportion of cheaters must decrease to even keep total resource use constant. Cost benefit analysis of the effect of regulation and incentives on potential cheaters may provide a rational approach to controlling environmental problems. While it is debatable that environmental values are constant across cultures, communal use of resources seems to follow global rules. Cooperative use and punishment of those who use more than their share appear to be ubiquitous in human societies. Schemes for controlling human impact on the global environment must take into consideration basic behaviours including development of social norms and the positive feedback created because resources become more valuable with increasing rarity leading to more incentive for consumption. (shrink)

Since Neumann and Morgenstern’s theory of games, the debate among social scientists, economists, mathematicians, and social philosophers about what kind of theory it is has not ended. Some think that it is a new interdiscipline, some that it is a mere accumulation of gametheoretical models, such as utility theory, competitive, cooperative, collective choice models, and so on. Most of them agree that the models of game theory deal with isolated, single, and independent specific societal (...) interactions between individuals who wish to maximize their gains and minimize their losses within prescribed constraining rules. (shrink)

Economists interpret global environmental quality to be a pure public good. Each country should contribute to its provision. However, this is hard to achieve because each government is tempted to take a free ride on the other governments' efforts. Not only has this dilemma been analysed with game theoretical methods but game theory has also been used to think about how to make amends. This paper reviews the game theoretical discussion on how international policy frameworks may (...) be designed to improve the chances for international cooperation. It is also shown that the evaluation of alternative environmental policy instruments deviates from the standard environmental economics model if applied to the international arena. For the benefit of an interdisciplinary readership, the evolution of the debate on global environmental policy is related to the recent history of economic thought. This history is taken to be materialised in the writings of economics' Nobel Prize laureates. (shrink)

Illustrates some of the successes of non‐cooperative game theory in economics. Specifically, it discusses how non‐cooperative game theory has helped economists to understand dynamic competition, credibility and reputation, cooperation based on reciprocity and the threat of punishment, and interactions in which parties hold private information, including information about their own basic motivations.

Game theory has proved to be a powerful research tool both in the social and in the natural sciences. Originally confined to the strategy of pure conflict, in zero-sum games, its field of application has been extended to cooperation, coordination and the whole range of strategic interactions in which conflict and cooperation coexist. One of its main achievements is a better understanding of how these interactions evolve and tend to become stable. Since it deals with the anticipation of (...) each other’s behaviour, love seems to be a promising field of analysis. And indeed, interesting research has been done on gift giving, commitment, strategies for mate choice, and other issues. The aim of this paper is to call attention to some of these recent developments. (shrink)

Is game theory good for us? This may seem an odd question. In the strict sense, game theory—the axiomatic account of interaction between rational agents—is as morally neutral as arithmetic. But the popularization of game theory as a way of thinking about social interaction is far from neutral. Consider the contrast between characterizing bargaining over distribution as a “zero-sum society” and focussing on “win-win” cooperative solutions. These reflections bring us to the book under (...) review, Prisoner's Dilemma, a popular introduction to game theory and its relation to ethics by the respected science writer William Poundstone. The book begins with a moral dilemma and ends by discussing the evolution of co-operation. Poundstone emphasizes—correctly, to my mind—the ethical potential of game theory. He concludes his first chapter with this striking claim: “Today's practitioners of game theory are attempting to forge a kind of ethical progress. Is there any way to promote the common good in a prisoner's dilemma? The attempt to answer this question is one of the great intellectual adventures of our time”. (shrink)

We study cooperative games in which the set of feasible coalitions is determined by the winning coalitions of a simple game. This type of game models real-life situations where certain agents have production capacities, while others possess the legal authority required to produce. In this paper, we characterize the Myerson value for this class of games by using five independent axioms. We show that the Myerson value is the only allocation rule on the set of voting structures (...) that satisfies efficiency, additivity, modularity, the extra-null player property, and equal treatment of veto. (shrink)

Game theory is central to modern understandings of how people deal with problems of coordination and cooperation. Yet, ironically, it cannot give a straightforward explanation of some of the simplest forms of human coordination and cooperation--most famously, that people can use the apparently arbitrary features of "focal points" to solve coordination problems, and that people sometimes cooperate in "prisoner's dilemmas." Addressing a wide readership of economists, sociologists, psychologists, and philosophers, Michael Bacharach here proposes a revision of game (...) theory that resolves these long-standing problems. In the classical tradition of game theory, Bacharach models human beings as rational actors, but he revises the standard definition of rationality to incorporate two major new ideas. He enlarges the model of a game so that it includes the ways agents describe to themselves their decision problems. And he allows the possibility that people reason as members of groups, each taking herself to have reason to perform her component of the combination of actions that best achieves the group's common goal. Bacharach shows that certain tendencies for individuals to engage in team reasoning are consistent with recent findings in social psychology and evolutionary biology. As the culmination of Bacharach's long-standing program of pathbreaking work on the foundations of game theory, this book has been eagerly awaited. Following Bacharach's premature death, Natalie Gold and Robert Sugden edited the unfinished work and added two substantial chapters that allow the book to be read as a coherent whole. (shrink)

A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. (...) In this paper we consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing properties. (shrink)

Evolutionary game theory and public goods games offer an important framework to understand cooperation during pandemics. From this perspective, the COVID-19 situation can be conceptualized as a dilemma where people who neglect safety precautions act as free riders, because they get to enjoy the benefits of decreased health risk from others’ compliance with policies despite not contributing to or even undermining public safety themselves. At the same time, humans appear to carry a suite of evolved psychological mechanisms aimed (...) at curbing free riding in order to ensure the continued provision of public goods, which can be leveraged to develop more effective measures to promote compliance with regulations. We also highlight factors beyond free riding that reduce compliance rates, such as the emergence of conspiratorial thinking, which seriously undermine the effectiveness of measures to suppress free riding. Together, the current paper outlines the social dynamics that occur in public goods dilemmas involving the spread of infectious disease, highlights the utility and limits of evolutionary game-theoretic approaches for COVID-19 management, and suggests novel directions based on emerging challenges to cooperation. (shrink)

Contents. Introduction. 1. Preliminaries. 2. Normal Form Games. 3. Extensive Games. 4. Applications of Game Theory. 5. The Methodology of Game Theory. Conclusion. Appendix. Bibliography. Index. Does game theory—the mathematical theory of strategic interaction—provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory—the first monograph on the philosophy of game theory—is an (...) attempt to combine insights from epistemic logic and the philosophy of science to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. I prove new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and explore in detail the logical form of game theory as it is used in explanatory and normative contexts. I argue that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, I argue, has been rather successful in achieving this aim. "The 'epistemic' approach to game theory has emerged over the past twenty-five years. What is this approach? How does it differ from the conventional equilibrium-based approach to game theory? What have been its strengths and weaknesses to date? To find out, read this comprehensive and excellently written account". Adam Brandenburger, J. P. Valles Professor of Business Economics and Strategy, Stern School of Business, New York University "Reading Boudewijn de Bruin's book should be rewarding both for game theorists interested in the conceptual foundations of their discipline and for philosophers who want to learn more about formal analysis of strategic interaction. It provides an in-depth logical study of the currently dominant epistemic approaches to non-cooperative games, with an eye both to the attractions and to the serious challenges facing the Epistemic Programme". Wlodek Rabinowicz, Professor of Practical Philosophy, Department of Philosophy, Lund University . (shrink)

In this paper, we study solution concepts for cooperative games with stochastic payoffs. we define four kinds of solution concepts, namely the most coalitional (marginal) stable solution and the fairest coalitional (marginal) solution, by minimizing the total variance of excesses of coalitions (individual players). All these four concepts are optimal solutions of corresponding optimal problem under the least square criterion. It turns out that the fairest coalitional (marginal) solution belongs to the set of the most coalitional (marginal) stable solutions. (...) Inspired by the definition of nucleolus, we propose various extended nucleolus based on lexicographic criterion. Furthermore, axiomatizations of the proposed solutions are exhibited through the linkage between the stochastic and deterministic models. (shrink)

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim (...) of this thesis is to enrich the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden, and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions. (shrink)

By focusing on players’ relative contributions, we study some properties for values in positive cooperative games with transferable utilities. The well-known properties of symmetry (also known as “equal treatment of equals”) and marginality are based on players’ marginal contributions to coalitions. Both Myerson’s balanced contributions property and its generalization of the balanced cycle contributions property (Kamijo and Kongo Int J of Game Theory 39:563–571, 2010; BCC) are based on players’ marginal contributions to other players. We define relative (...) versions of marginality and BCC by replacing marginal contributions with relative contributions, and examine efficient values satisfying each of the two properties. On the class of positive games, a relative variation of marginality is incompatible with efficiency, and together with efficiency and the invariance property with respect to the payoffs of players under a player deletion, a relative variation of BCC characterizes the proportional value and egalitarian value in a unified manner. (shrink)

Virtual bargaining theory suggests that social agents aim to resolve non-cooperative games by identifying the strategy profile which they would agree to play if they could openly bargain. The theory thus offers an explanation of how social agents resolve games with multiple Nash equilibria. One of the main questions pertaining to this theory is how the principles of the bargaining theory could be applied in the analysis of hypothetical bargaining in non-cooperative games. I propose (...) a bargaining model based on the benefit-equilibrating bargaining solution concept for non-cooperative games, broadly in line with the principles underlying Conley and Wilkie's ordinal egalitarian solution for Pareto optimal point selection problems with finite choice sets. I provide formal characterizations of the ordinal and the cardinal versions of BES, discuss their application to n-player games, and compare model's theoretical predictions with the data available from several experiments involving `pie games'. (shrink)

The model of incomplete cooperative games incorporates uncertainty into the classical model of cooperative games by considering a partial characteristic function. Thus the values for some of the coalitions are not known. The main focus of this paper is 1-convexity under this framework. We are interested in two heavily intertwined questions. First, given an incomplete game, how can we fill in the missing values to obtain a complete 1-convex game? Second, how to determine in a rational, (...) fair, and efficient way the payoffs of players based only on the known values of coalitions? We illustrate the analysis with two classes of incomplete games—minimal incomplete games and incomplete games with defined upper vector. To answer the first question, for both classes, we provide a description of the set of 1-convex extensions in terms of its extreme points and extreme rays. Based on the description of the set of 1-convex extensions, we introduce generalisations of three solution concepts for complete games, namely the τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}-value, the Shapley value and the nucleolus. For minimal incomplete games, we show that all of the generalised values coincide. We call it the average value and provide different axiomatisations. For incomplete games with defined upper vector, we show that the generalised values do not coincide in general. This highlights the importance and also the difficulty of considering more general classes of incomplete games. (shrink)

Thomas Schelling, who wrote the foreword for this book, won the Nobel Prize in economics for "having enhanced our understanding of conflict and cooperation through game-theory analysis." This came after he had taught a course in game theory and rational choice to advanced students and government officials for 45 years. In this book, Robert Dodge provides in language for a broad audience, the concepts that Schelling taught. Armed with Schelling's understanding of game theory methods (...) and his approaches to problems, the general reader can improve daily decision making. Mathematics often make game theory challenging but was not a major part of Schelling's course and is even less of a factor in this book. Along with a summary of the material Schelling presented, included are problems from the course and similar less challenging questions. While considerable analysis is done with the basic game theory tool--the two-by-two matrix--much of the book is descriptive and rational decision-making is explained with stories. Chapter supplements are added to illuminate points presented by Schelling, including writings by Paul Krugman, Thomas Friedman, Steven Levitt, and others. (shrink)

This article is a contribution to a symposium celebrating the life of Patrick Suppes. It describes the context in which he made contributions relevant to two extremes of the game theory spectrum. At one extreme, he made an experimental study of whether laboratory subjects learn to use Von Neumann’s minimax theory in games of pure conflict. At the other extreme, he invented a theory of empathetic identification that lies at the root of an approach to making (...) interpersonal comparisons needed for the study of games in which cooperation is central rather than conflict. These pieces of work are peripheral to his major interests, but they nevertheless illustrate how it is possible to be an academic success without conceding anything to current academic fashion. (shrink)

A computer simulation runs a model generating a phenomenon under investigation. For the simulation to be explanatory, the model has to be explanatory. The model must be isomorphic to the natural system that realizes the phenomenon. This paper elaborates the method of assessing a simulation's explanatory power. Then it illustrates the method by applying it to two simulations in game theory. The first is Brian Skyrms's (1990) simulation of interactive deliberations. It is intended to explain the emergence of (...) a Nash equilibrium in a noncooperative game. The second is Skyrms's (2004) simulation of the evolution of cooperation. It is intended to explain cooperation in assurance games. The final section suggests ways of enhancing the explanatory power of these simulations. (shrink)

Psychological game theory encompasses formal theories designed to remedy game-theoretic indeterminacy and to predict strategic interaction more accurately. Its theoretical plurality entails second-order indeterminacy, but this seems unavoidable. Orthodox game theory cannot solve payoff-dominance problems, and remedies based on interval-valued beliefs or payoff transformations are inadequate. Evolutionary game theory applies only to repeated interactions, and behavioral ecology is powerless to explain cooperation between genetically unrelated strangers in isolated interactions. Punishment of defectors elucidates cooperation (...) in social dilemmas but leaves punishing behavior unexplained. Team reasoning solves problems of coordination and cooperation, but aggregation of individual preferences is problematic. (shrink)

We present a theory of cooperative-competitive intelligence (CCI), its measures, research program, and applications that stem from it. Within the framework of this theory, satisficing sub-optimal behavior is any behavior that does not promote a decrease in the prospective control of the functional action diversity/unpredictability (D/U) potential of the agent or team. This potential is defined as the entropy measure in multiple, context-dependent dimensions. We define the satisficing interval of behaviors as CCI. In order to manifest itself (...) at individual or team level, this capacity harnesses properties such as degeneracy, pleiotropy (pluri-potentiality), synergies, and metastability. Intelligence is embodied because intelligent behavior is deeply dependent on body functionalities, defined as entropy measures. We base our theory on three principles: (a) relativity of functional entropy/ information in agent (team)-environment systems, (b) tendency toward the satisficing level of D/U potential, and (c) tendency toward the non-decreasing D/U potential. The conjunction of these three principles provides existence of sub-optimal behaviors associated with CCI. First, we deal with the problem of how to reduce multidimensional behavior to a concept that accounts for the vast set of scenarios in which CCI is manifested. Secondly, we define and discuss the three interacting principles that underpin CCI behavior as well as providing an outline for a future CCI research program supported by agent￾based modeling and empirical research. Finally, we provide some preliminary practical issues that stem from the theory. (shrink)

The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', (...) 'self-evident', and 'justifiable'. I also construct in modal operator logic a paradox involving reflexive empirical reasoning. Unlike the paradox of the Liar, the paradox of reflexive reasoning does not depend on self-reference. ;I consider various solutions to the Liar paradox and evaluate how well these solutions cope with the paradox of reflexive reasoning. I then formalize the solution to the paradoxes which I favor: the indexical-hierarchical approach, first sketched out by Charles Parsons and Tyler Burge. In this solution, occurrences of the predicate 'true' in sentence-tokens are contextually relativized to levels of a hierarchy. Drawing also on some brief remarks of Bertrand Russell and Charles Parsons, I develop an account of the kind of schematic generality needed for this theory to be statable. ;Finally, I demonstrate that the principles shown to be paradoxical are in fact presupposed by contemporary game theorists in their reliance on the notion of common knowledge or, more precisely, mutual belief. I create novel analyses of and corresponding solutions to several recalcitrant puzzles within game theory, including the "chain-store paradox". (shrink)

Evolutionary game theory is ethically neutral: its assumption of ‘rationality’ has nothing to do with selfishness but is in fact entirely compatible with altruism. If altruism has an evolutionary explanation then this fact is of no theological relevance: in particular it is not any sort of evidence of a divine plan etc.

Cooperation has been analyzed primarily in the context of theories of collective intentionality. These discussions have primarily focused on interactions between pairs or small groups of agents who know one another personally. Cooperative game theory has also been used to argue for a form of cooperation in large unorganized groups. Here I consider a form of minimal cooperation that can arise among members of potentially large organized groups (e.g., corporate teams, committees, governmental bodies). I argue that members (...) of organized groups can be minimally cooperative in virtue of playing roles in an organizational structure and having a common goal. The minimal form of cooperation I argue for is not grounded in collective intentions involving symmetric mental states, special collective intentional modes, or joint commitments. More generally, I show how considering minimal cooperation in the context of organized groups provides an opportunity to reevaluate the extent to which the social world and social phenomena depend on internalist mental factors (e.g., intentions, beliefs) and externalist non-mental factors (e.g., documents, laws, job descriptions). The view of minimal cooperation among members of organized groups I offer provides support for an externalist rather than internalist theory of at least one social phenomenon. (shrink)

Both terrorism and game theory are contested concepts within the social sciences, but in this paper, I will show that a rational approach (game theory) towards the emotion-laden idea and practice of terrorism does aid understanding of the “terrorist theatre”. First, an outline will be provided on the type of actors (game players) that are, or may be, involved to a more or lesser extend in (supporting) terrorism. Then several game models will be assessed (...) on their applicability. This includes averting the joint bargaining paradox when asymmetric actors cooperate to achieve a joint goal, governments who may fare better from their point of view when dividing up refugees into geographically separate areas to decrease the possibility of cooperation between aggrieved groups and recognizing two-speed negotiations, which can have a (detrimental) effect on (deadline) negotiations. Further, an adaptation of the audience cost model explained the “war of nerves” of the terrorist theatre involving the generation of fear amongst its targets and the updating of information on moderate actors by action of extremists. Several mutations of the Prisoner’s Dilemma were discussed as options to prevent mutual harm. (shrink)

The aim of this paper is to critically review the game-theoretic discussion of Hobbes and to develop a game-theoretic interpretation that gives due attention both to Hobbes's distinction between “moderates” and “dominators” and to what actually initiates conflict in the state of nature, namely, the competition for vital goods. As can be shown, Hobbes's state of nature contains differently structured situations of choice, the game-theoretic representation of which requires the prisoner's dilemma and the assurance game and (...) the so-called assurance dilemma. However, the “state of war” ultimately emerges from situations that cannot be described by any of these games because they represent zero-sum games in which the outcome of mutual cooperation does not exist. (shrink)

This paper assesses the theory, first voiced by Schelling and Kant, according to which an infinite historical process will lead to cosmopolitan institutions.The assessment will mainly be done on the basis of theories about infinitely repeated games. The first part of the paper reconstructs “infinitesimal” historical cosmopolitanism as proposed by Schelling and Kant. The second part confronts this position with the results of the theory of infinitely repeated games among groups. The third part offers reflections on additional conditions (...) and contingencies of the theory and the forth part draws the conclusion: while we can reasonably assume global cooperation to increase and stabilize over time under sustainable conditions, we cannot predict the institutional design of that cooperation. (shrink)

The importance of the notion of common knowledge in sustaining cooperative outcomes in strategic situations is well appreciated. However, the systematic analysis of the extent to which small departures from common knowledge affect equilibrium in games has only recently been attempted.We review the main themes in this literature, in particular, the notion of common p-belief. We outline both the analytical issues raised, and the potential applicability of such ideas to game theory, computer science and the philosophy of (...) language. (shrink)

This paper considers whether the available evidence from archeology, biological anthropology, primatology, and comparative gene-sequencing, can test evolutionary game theory models of cooperation as historical hypotheses about the actual course of human prehistory. The examination proceeds on the assumption that cooperation is the product of cultural selection and is not a genetically encoded trait. Nevertheless, we conclude that gene sequence data may yet shed signi cant light on the evolution of cooperation.