Game Theory

Game theory extends classical decision theory by focusing on situations in which an actor's result depends not only on his or her own decisions but also on one or more persons' behavior. In this sense, it is a theory of social interaction with a special interest in goal-directed (“rational”) behavior.

“Born” by John von Neumann and Oskar Morgenstern (1944), applications of game theory spread from economics to political science, psychology, sociology, and even biology. Key elements of game-theoretic studies are games, players, strategies, payoffs, and maximization. A “game” describes a given situation of social interaction between at least two actors (“players”) with all the rules of the game, as well as its possibilities and restrictions. The situation offers the players various alternatives to decide and act (“strategies”). The players' strategies lead to different outcomes along with different utility values (“payoffs”). Based on these key elements, game-theoretic analysis can show which strategy a player will choose when he or she maximizes his or her payoff. Therefore, game theory is more a mathematical discipline than a psychological theory.

Although goal-directed behavior is a presumption of game theory, theoretical results and empirical evidence sometimes can be bizarre. A famous example is the PRISONER'S DILEMMA (PD). The PD is a simple model of a situation of strategic interdependence with aspects of cooperation and conflict. Table 1 shows the PD that Robert Axelrod (1984) used in his computer tournament. Individually seen, defection always leads to a better payoff than cooperation (and is therefore a “dominant strategy”). The dilemma is that although mutual defection causes a worse result than mutual cooperation, a player has no interest in a one-sided change of his or her strategy. With this characterization, the PD can be a fruitful model of various social situations such as employment relations, an arms race, or free trade. It also illustrates that game-theoretical analysis is most interesting in situations with mixed motives of cooperation and conflict incentives.

Looking at classical methods of data collection, most empirical game-theoretical studies use EXPERIMENTS, COMPUTER SIMULATIONS, and—in a broader sense—CONTENT ANALYSIS. In a content analysis, given documents such as statistics or historical data are analyzed to build a game-theoretic model (e.g., an explanation of political strategic moves at the beginning of World War I). Computer simulations can match a variety of different strategies to simulate the effect of repeated games (iterations), changed parameters, or evolution aspects. Experiments are the best way of testing (game) theoretical findings. The study by Anatol Rapoport and Albert Chammah (1965) about the PD exemplifies the connection of theoretical, experimental, and simulation aspects. For a general introduction, see Gintis (2000).