The Prisoner's Dilemma (PD) exhibits a tragedy in this sense: if the players are fully informed and rational, they are condemned to a jointly dispreferred outcome. In this essay I address the following question: What feature of the PD's payoff structure is necessary and sufficient to produce the tragedy? In answering it I use the notion of a trembling-hand equilibrium. In the final section I discuss an implication of my argument, an implication which bears on the persistence of the problem (...) posed by the PD. (shrink)

We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to 1-x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-x$$\end{document}, where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between these two (...) extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four. (shrink)

Strong Nash equilibrium and coalition-proof Nash equilibrium rely on the idea that players are allowed to form coalitions and make joint deviations. Both of these notions consider cases in which any coalition can be formed. Accordingly, there may arise “conflicts of interest” that prevent a player from choosing an action that simultaneously meets the requirements of two coalitions to which he or she belongs. Here, we address this observation by studying an organizational framework such that the coalitional structure is motivated (...) by real-life examples where players cannot form some coalitions and formulated in such a way that no conflicts of interest remain. We define an organization as an ordered collection of partitions of the player set such that any partition is coarser than the partitions that precede it. For any given organization, we introduce the notion of organizational Nash equilibrium. We analyze the existence of equilibrium in a subclass of games with strategic complementarities and illustrate how the proposed notion refines the set of Nash equilibria in some examples of normal form games. (shrink)

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

In a conflict between two people, one person wants one thing and the other wants something else and they think they can't both have what they want. Suppose that what they want can only be the outcome of some joint action. Adam must do either y or z and Eve either y ' or z ' – here y -and- y ' would be one joint action, y -and- z ' would be another, and so on. Adam wants the outcome (...) of his doing z while Eve is doing y '. Eve wants the outcome of her doing z ' while Adam is doing y. Each thinks that these outcomes can't both be had. (shrink)

We implement a risky choice experiment based on one-dimensional choice variables and risk neutrality induced via binary lottery incentives. Each participant confronts many parameter constellations with varying optimal payoffs. We assess optimality, as well as optimal satisficing by eliciting aspirations in addition to choices. Treatments differ in the probability that a binary random event, which are payoff—but not optimal choice—relevant is experimentally induced and whether participants choose portfolios directly or via satisficing, i.e., by forming aspirations and checking for satisficing before (...) making their choice. By incentivizing aspiration formation, we can test satisficing, and in cases of satisficing, determine whether it is optimal. (shrink)

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)

Gupta has proposed a definition of strategic rationality cast in the framework of his revision theory of truth. His analysis, relative to a class of normal form games in which all players have a strict best reply to all other players’ strategy profiles, shows that game-theoretic concepts have revision-theoretic counterparts. We extend Gupta’s approach to deal with normal form games in which players’ may have weak best replies. We do so by adapting intuitions relative to Nash equilibrium refinements to the (...) revision-theoretic framework. We prove that there is a precise equivalence between trembling-hand perfect equilibria in two-player normal games and a revision-theoretic property. We then introduce lexicographic choice of action as a way to represent players’ expectations, which allows our analysis to reach full generality. Finally, we provide an example of the versatility of revision theory as applied to strategic interaction by formalizing a risk-and-compensation procedure of strategic choice in the revision-theoretic framework. (shrink)

Game theory has proved a useful tool in the study of simple economic models. However, numerous foundational issues remain unresolved. The situation is particularly confusing in respect of the non-cooperative analysis of games with some dynamic structure in which the choice of one move or another during the play of the game may convey valuable information to the other players. Without pausing for breath, it is easy to name at least 10 rival equilibrium notions for which a serious case can (...) be made that here is the “right” solution concept for such games. (shrink)

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

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)

‘Noise’ in this study, in the sense of evolutionary game theory, refers to deviations from prevailing behavioral rules. Analyzing data from a laboratory experiment on coordination in networks, we tested ‘what kind of noise’ is supported by behavioral evidence. This empirical analysis complements a growing theoretical literature on ‘how noise matters’ for equilibrium selection. We find that the vast majority of decisions constitute myopic best responses, but deviations continue to occur with probabilities that are sensitive to their costs, that is, (...) less frequent when implying larger payoff losses relative to the myopic best response. In addition, deviation rates vary with patterns of realized payoffs that are related to trial-and-error behavior. While there is little evidence that deviations are clustered in time or space, there is evidence of individual heterogeneity. (shrink)