Game Theory and Psychology - Psychology - Oxford Bibliographies Game Theory and Psychology Andrew M. Colman, Eva M. Krockow LAST MODIFIED: 27 JUNE 2017 DOI: 10.1093/OBO/9780199828340-0192 Introduction Game theory is a branch of decision theory focusing on interactive decisions, applicable whenever the actions of two or more decision makers jointly determine an outcome that affects them all. Strategic reasoning amounts to deciding how to act to achieve a desired objective, taking into account how others will act and the fact that they will also reason strategically. The primitive concepts of the theory are players (decision makers), strategies (alternatives among which each player chooses), and payoffs (numerical representations of the players’ preferences among the possible outcomes of the game). The theory’s fundamental assumptions are (i) that all players have consistent preferences and are instrumentally rational in the sense of invariably choosing an alternative that maximizes their individual payoffs, relative to their knowledge and beliefs at the time and (ii) that the specification of the game and the players’ preferences and rationality are common knowledge among the players (explained under Common Knowledge). Game theory amounts to working out the implications of these assumptions in particular classes of games and thereby determining how rational players will act. Psychology is the study of the nature, functions, and phenomena of behavior and mental experience, and two branches of psychology provide bridges to and from game theory: cognitive psychology, concerned with all forms of cognition, including decision making, and social psychology, concerned with how individual behavior and mental experience are influenced by other people. Psychology uses empirical research methods, including controlled experiments, and its usefulness for studying games emerges from three considerations. First, many games turn out to lack determinate game-theoretic solutions, and psychological theories and empirical evidence are therefore required to discover and understand how people play them. Second, human decision makers have bounded rationality and are rarely blessed with full common knowledge; consequently, except in the simplest cases, they do not necessarily choose strategies that maximize their payoffs even when determinate game-theoretic solutions exist. Third, human decision makers have other-regarding preferences and sometimes do not even try to maximize their personal payoffs, without regard to the payoffs of others, and psychological theory and empirical research are therefore required to provide a realistic account of real-life strategic interaction. Psychology has investigated strategic interaction since the 1950s; behavioral game theory, a branch of the emergent subdiscipline of behavioral economics, has used similar techniques since the late 1980s. General Overviews of Game Theory There are many excellent textbooks devoted to game theory and behavioral game theory, varying in their levels of mathematical difficulty and relevance to psychology. Luce and Raiffa 1957 is the most influential and widely read early text, and it has remained useful for succeeding generations of students and researchers. It offers an excellent introduction to standard concepts of game theory, including Nash equilibrium, the most fundamental solution concept for games of all types. A Nash equilibrium is an outcome of any game in which the strategy chosen by each player is a best reply to the strategies chosen by the other player(s), in the sense that no other choice would have yielded a better payoff, given the strategy choices of the other player(s), and as a consequence no player has cause to regret the chosen strategy when the outcome is revealed. Binmore 1991 is useful for mathematically minded beginners and more Game Theory and Psychology - Psychology - Oxford Bibliographies advanced readers, and the simpler text Gibbons 1992 conveys the basic mathematics more briefly. Colman 1995 reviews the fundamental ideas of game theory and related experimental research from a psychological perspective. Camerer 2003 provides the first wide-ranging survey of behavioral game theory in book form. In an influential monograph, Schelling 1960 uses game theory brilliantly to illuminate psychological features of human strategic interaction. Binmore, K. 1991. Fun and games: A text on game theory. Lexington, MA: Heath. This is a basic text on mathematical game theory written by a leading game theorist. It presents mathematical aspects of the theory exceptionally clearly, and readers with a basic knowledge of school mathematics should be able to understand it. Parts of it are far from elementary, making it interesting and informative even for readers with an intermediate-level understanding of game theory. Binmore, K. 2007. Game theory: A very short introduction. Oxford: Oxford Univ. Press. This very short introduction to the formal aspects of the theory outlines the basic ideas in an easily digestible form. Camerer, C. F. 2003. Behavioral game theory: Experiments in strategic interaction. Princeton, NJ: Princeton Univ. Press. This is a magisterial review of almost the whole of behavioral game theory up to the early 2000s. This book covers many key topics in remarkable depth, and much of it is essentially psychological in flavor. Colman, A. M. 1995. Game theory and its applications in the social and biological sciences. 2d ed. London: Routledge. This monograph presents the basic ideas of game theory from a psychological perspective, reviews experimental evidence up to the mid-1990s, and discusses applications of game theory to voting, evolution of cooperation, and moral philosophy. An appendix contains the most elementary available self-contained proof of the minimax theorem (see Strategic Reasoning Before Game Theory). The first edition was published in 1982. Gibbons, R. 1992. A primer in game theory. Hemel Hempstead, UK: Harvester Wheatsheaf. A more orthodox and slightly simpler and shorter basic text on mathematical game theory than Binmore 1991, widely prescribed in standard university courses and easily accessible to readers with a basic knowledge of school mathematics. Luce, R. D., and H. Raiffa. 1957. Games and decisions: Introduction and critical survey. New York: Wiley. This was the text that first brought game theory to the attention of behavioral and social scientists, being much more accessible than the book by von Neumann and Morgenstern 1944 (cited under Strategic Reasoning Before Game Theory) that had preceded it. It is a brilliant textbook with some simple mathematical content, and it has remained highly relevant and useful for subsequent generations of researchers and scholars. Schelling, T. C. 1960. The strategy of conflict. Cambridge, MA: Harvard Univ. Press. This fascinating monograph, by a psychologically minded economist, was largely responsible for its author’s Nobel Prize. It has hardly any mathematical content but instead uses the conceptual framework of game theory to focus on aspects of interactive decision making that lie outside the formal theory. This is a must-read for anyone interested in game theory in psychology. It was reprinted with a new preface in 1980. Game Theory and Psychology - Psychology - Oxford Bibliographies Strategic Reasoning before Game Theory The emergence of game theory is usually traced back to a proof in von Neumann 1928 of a key theorem (the minimax theorem, establishing the existence of, and characterizing, what were later called “Nash equilibria” for strictly competitive games) or to the first edition of Theory of Games and Economic Behavior (von Neumann and Morgenstern 1944). However, early records confirm that people had been aware of problems of strategic interaction in historical times. For example, the Babylonian Talmud, one of the core texts of Rabbinic Judaism, written in the 3rd to the 5th centuries CE, contains a detailed discussion of the fairest way to divide up the estate of a person who dies owing several creditors different amounts, the total owed exceeding the value of the estate, and the solution that is suggested (not simple proportionality) seems counterintuitive and baffled scholars for centuries. Aumann and Maschler 1985 shows that the Talmudic suggestion coincides with a game-theoretic solution called the “nucleolus,” the full mathematical details of which were first worked out and published in Schmeidler 1969. Evidence also exists of strategic reasoning in the Bible (see Games of Strategy in the Bible) and in ancient Rome (see Strategic Voting in Ancient Rome). Aumann, R. J., and M. Maschler. 1985. Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36.2: 195–213. This article, the first author of which is the Nobel laureate and game theorist Robert J. Aumann, describes the problem of dividing up a bankrupt estate among creditors. It shows, in easily understood language, how the solution recommended in the Babylonian Talmud, which deviates from simple proportionality, coincides with the nucleolus of Schmeidler 1969. Schmeidler, D. 1969. The nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 17.6: 1163–1170. This is the original presentation of the theory of the nucleolus, considered an important though advanced “solution concept” for a particular class of games. von Neumann, J. 1928. Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100.1: 295–320. This article marks the emergence of game theory, according