Game Theory

Game theory is the study of rational behavior in situations of interactive decision making—that is, situations in which two or more individuals make decisions that jointly determine an outcome about which the participants have differing preferences or information. As a theory, it aims to articulate the criteria and implications of such decision making, defining principles of idealized strategic choice. These principles can then be used to clarify explanatory and normative concepts of human interaction. An experimental branch examines the extent to which real decision makers in a laboratory setting realize those principles and identifies regular patterns of departure from them. As an empirical tool, game theoretic models of social phenomena yield empirical predictions suitable for testing with observational data. Originally applied to economics, game theory has found application across the social sciences, as well as in biology (where in effect the “selfish gene” and natural selection replace individual strategic decision making) and literary theory (where game theory principles have been used to explicate portrayals of conflict and cooperation, as well as the interaction between author and reader).

Following scattered preliminaries during the period from 1910 to 1927, game theory was essentially created by the mathematician John von Neumann in a paper published in 1928 defining strategic play in finite games of pure conflict with two players. In collaboration with the economist Oskar Morgenstern, von Neumann authored Games and Economic Behavior (published in 1944), further developing the theory and beginning its application to problems of economic interaction. Rapid theoretical development followed World War II, and the theory made its first scattered appearances in the political science journals in the 1950s. By the 1980s, game theory had become the primary model-building tool of rational choice political science, with applications in virtually all subfields. International relations saw some of the earliest use of game theory, which came to be especially common in the study of crisis bargaining and the inception of war. The scholars of U.S. politics were also early adopters, applying game theory extensively to legislative processes, electoral competition, and even school budget referendum politics. Many of the American politics applications were generalized to similar questions concerning legislative and electoral politics in comparative perspective, but game theoretic applications to coalition formation, class relations, and ethnic politics were pioneered in comparative politics. In political theory, game theoretic tools were proving useful for gaining new normative understanding in areas such as collective action and constitutionalism.

Game theory itself consists of two main branches: (1) noncooperative and (2) cooperative. Noncooperative game theory focuses on individual decisions, dwelling on problems of strategic moves and incentives, and attempting to explain not only conflict and competition but also the attainment of commitment, coordination, or cooperation in groups. This entry dwells mostly on the [Page 948]noncooperative branch, constructing in detail the two major formulations used there, namely, the strategic and sequential forms; the major theories of how each form of game is solved; and the correspondences between them. Cooperative game theory focuses on the abilities and actions of coalitions, often assuming that coordination and cooperation can be attained as needed and asking how they will be employed to realize and distribute gains or losses. Cooperative game theory may be taken to subsume not only coalition games but also the foundations of social choice theory and voting theory, although the latter have important overlaps with noncooperative theory as well. The final section summarizes the basic features of the fundamental cooperative game formulation, the characteristic function form.

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