Outcome (game theory)

In game theory, an outcome is a set of moves or strategies taken by the players, or their payoffs resulting from the actions or strategies taken by all players. The two are complementary in that, given knowledge of the set of strategies of all players, the final state of the game is known, as are any relevant payoffs. In a game where chance or a random event is involved, the outcome is not known from only the set of strategies, but is only realized when the random event(s) are realized.

A set of payoffs can be considered a set of N-tuples, where N is the number of players in the game, and the cardinality of the set is equal to the total number of possible outcomes when the strategies of the players are varied. The payoff set can thus be partially ordered, where the partial ordering comes from the value of each entry in the N-tuple. How players interact to allocate the payoffs among themselves is a fundamental aspect of economics.

Choosing among outcomes

Many different concepts exist to express how players might interact. An optimal interaction might be one in which no player's payoff can be made greater, without making any other player's payoff lesser. Such a payoff is called Pareto efficient, and the set of such payoffs is called the Pareto frontier.

Many economists study the ways in which payoffs are in some sort of economic equilibrium. One example of such an equilibrium is the Nash equilibrium, where each player plays a strategy such that their payoff is maximized given the strategy of the other players.

Applications

Equilibria are not always Pareto efficient, and a number of game theorists design ways to enforce Pareto efficient play, or play that satisfies some other sort of social optimality. The theory of this is called implementation theory. Other economists seek to design games based on a certain set of outcomes, an effort which goes under the name of mechanism design.

This game theory article is a stub. You can help Wikipedia by expanding it.v · Categories: Game theory Economics and finance stubs Wikimedia Foundation. 2010. Игры ⚽ Нужно сделать НИР? Mechanism (sociology) Winslow Corbett Look at other dictionaries: game theory — a mathematical theory that deals with strategies for maximizing gains and minimizing losses within prescribed constraints, as the rules of a card game: widely applied in the solution of various decision making problems, as those of military… …   Universalium game theory — The general theory of the rational behaviour of two or more people in circumstances where their interests are, at least in part, conflicting. In The Theory of Games and Economic Behaviour(1947), John Von Neumann and Oskar Morgenstern attempted to …   Dictionary of sociology game theory — A mathematical theory, developed by J. von Neumann (1903 57) and O. Morgenstern (1902 77) in 1944, concerned with predicting the outcome of games of strategy (rather than games of chance) in which the participants have incomplete information… …   Big dictionary of business and management Dominance (game theory) — In game theory, dominance (also called strategic dominance) occurs when one strategy is better than another strategy for one player, no matter how that player s opponents may play. Many simple games can be solved using dominance.The opposite,… …   Wikipedia Generalized game theory — is an extension of game theory to incorporate social theory concepts such as norm, value, belief, role, social relationship, and institution. The theory was developed by Tom R. Burns and has not had great influence beyond his immediate associates …   Wikipedia Glossary of game theory — Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. This is a glossary of some terms of the subject. Definitions of a game Notational conventions ; Real numbers : mathbb{R} .; The set… …   Wikipedia List of games in game theory — Game theory studies strategic interaction between individuals in situations called games. Classes of these games have been given names. This is a list of the most commonly studied games.Explanation of featuresGames can have several features, a… …   Wikipedia game theory — The mathematical theory of situations in which two or more players have a choice of decisions (strategies); where the outcome depends on all the strategies; and where each player has a set of preferences defined over the outcomes. See also… …   Philosophy dictionary game theory — noun the mathematical study of strategies for dealing with competitive situations where the outcome of a participant s choice of action depends critically on the actions of other participants. Compare with decision theory …   English new terms dictionary Folk theorem (game theory) — infobox equilibrium name= Folk theorem subsetof = Minimax, Nash Equilibrium discoverer = various, notably Ariel Rubinstein usedfor = Infinitely repeated games example = Repeated prisoner s dilemma In game theory, folk theorems are a class of… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”