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Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science.
- Overview
- Classification of games
- One-person games
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game theory, branch of applied mathematics that provides tools for analyzing situations in which parties, called players, make decisions that are interdependent. This interdependence causes each player to consider the other player’s possible decisions, or strategies, in formulating strategy. A solution to a game describes the optimal decisions of the players, who may have similar, opposed, or mixed interests, and the outcomes that may result from these decisions.
Although game theory can be and has been used to analyze parlour games, its applications are much broader. In fact, game theory was originally developed by the Hungarian-born American mathematician John von Neumann and his Princeton University colleague Oskar Morgenstern, a German-born American economist, to solve problems in economics. In their book The Theory of Games and Economic Behavior (1944), von Neumann and Morgenstern asserted that the mathematics developed for the physical sciences, which describes the workings of a disinterested nature, was a poor model for economics. They observed that economics is much like a game, wherein players anticipate each other’s moves, and therefore requires a new kind of mathematics, which they called game theory. Game theory was further developed in the 1950s by American mathematician John Nash, who established the mathematical principles of game theory, a branch of mathematics that examines the rivalries between competitors with mixed interests. (The name for this branch of studies may be somewhat of a misnomer—game theory generally does not share the fun or frivolity associated with games.)
(Read Steven Pinker’s Britannica entry on rationality.)
Game theory has been applied to a wide variety of situations in which the choices of players interact to affect the outcome. In stressing the strategic aspects of decision making, or aspects controlled by the players rather than by pure chance, the theory both supplements and goes beyond the classical theory of probability. It has been used, for example, to determine what political coalitions or business conglomerates are likely to form, the optimal price at which to sell products or services in the face of competition, the power of a voter or a bloc of voters, whom to select for a jury, the best site for a manufacturing plant, and the behaviour of certain animals and plants in their struggle for survival. It has even been used to challenge the legality of certain voting systems.
Games can be classified according to certain significant features, the most obvious of which is the number of players. Thus, a game can be designated as being a one-person, two-person, or n-person (with n greater than two) game, with games in each category having their own distinctive features. In addition, a player need not be an individual; it may be a nation, a corporation, or a team comprising many people with shared interests.
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In games of perfect information, such as chess, each player knows everything about the game at all times. Poker, on the other hand, is an example of a game of imperfect information because players do not know all of their opponents’ cards.
The extent to which the goals of the players coincide or conflict is another basis for classifying games. Constant-sum games are games of total conflict, which are also called games of pure competition. Poker, for example, is a constant-sum game because the combined wealth of the players remains constant, though its distribution shifts in the course of play.
Players in constant-sum games have completely opposed interests, whereas in variable-sum games they may all be winners or losers. In a labour-management dispute, for example, the two parties certainly have some conflicting interests, but both will benefit if a strike is averted.
One-person games are also known as games against nature. With no opponents, the player only needs to list available options and then choose the optimal outcome. When chance is involved the game might seem to be more complicated, but in principle the decision is still relatively simple. For example, a person deciding whether to carry an umbrella wei...
Game theory is a branch of mathematics that analyzes situations in which parties make interdependent decisions. Learn about the history, classification, and applications of game theory, as well as its concepts and methods.
Jan 25, 1997 · Game theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents.
Jun 2, 2003 · Learn what game theory is, how it models competitive situations with rules and strategies, and what are some of its real-world examples. Explore the concepts of zero-sum games, optimal strategies, and value of the game with examples and exercises.
May 14, 2024 · Game theory is a branch of mathematics that explores how people make decisions and compares them with mathematical models. Read on to learn more about game theory, including examples and its applications in law, economics, software, and more.
Learn the basics of game theory, the mathematical analysis of decision making in situations with multiple players. Explore examples of games, such as the prisoner's dilemma and the stag hunt, and their Nash equilibria and iterations.
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