Graph Theory
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GA ▶ Genetic Algorithms
Game Theory William F. Lucas1 and Sauleh A. Siddiqui2 1 Claremont Graduate University, Claremont, CA, USA 2 University of Maryland, College Park, MD, USA
Introduction Game theory studies situations involving conflict and cooperation. The three main elements of a game are players, strategies, and payoffs. Games arise when two or more decision makers (players) select from various courses of action (called strategies) which in turn result in likely outcomes (expressed as payoffs). There must be at least two interacting participants with different goals in order to have a game. Game theory makes use of the vocabulary from common parlor games and sports. It is, nevertheless, a serious mathematical subject with a broad spectrum of applications in the social, behavioral, managerial, financial, system, and military sciences. Game theory differs from classical optimization subjects in that it involves two or more players with different objectives. It also extends the traditional uses of probability and statistics beyond the study of one-person decisions in the realm of statistical uncertainty. This latter case is often referred to as
games of chance or games against nature in contrast to the games of skill studied in game theory. Many aspects of social and physical science can be viewed as zero-person games since actions are frequently specified by various laws that are not under human control. Game theory presumes that conflict is not an evil in itself and as such unworthy of study. Rather, that this topic arises naturally when individuals have free will, different desires, and the freedom of choice. Furthermore, this subject often provides guidelines to aid in the resolution of conflict. Game theory also assumes that the players can quantify potential outcomes (as in measurement theory or utility theory), that they are rational in the sense that they seek to maximize their payoffs, and skillful enough to undertake the necessary calculations. The theory of games attempts to describe what is optimal strategic behavior, the nature of equilibrium outcomes, the formation and stability of coalitions, as well as fairness. There are many different ways to classify games. A significant difference exists between the two-person games and the multiperson ones (also called the n-person games when n 3). There is a major distinction depending upon whether games are played in a cooperative or noncooperative manner. The nature of the types or amount of information available to the players is very fundamental in the analysis of games, and this relates to whether the best way to play involves pure or randomized strategies. A further way to classify games is if they are played over one period or repeatedly over time. Static games are single period games in which all players move simultaneously without observing any other moves.
S.I. Gass, M.C. Fu (eds.), Encyclopedia of Operations Research and Management Science, DOI 10.1007/978-1-4419-1153-7, # Springer Science+Business Media New York 2013
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