extensive form game

extensive form game
Informally, a representation of a game as a tree of decision nodes, with the game beginning at a unique initial node, and flowing through the tree along a path determined by the players until a terminal node is reached, where play ends and payoffs are assigned to all players; each non-terminal node belongs to a player; that player chooses among the possible moves at that node, each possible move is an edge leading from that node to another node. <! The formal definition is even longer than that.

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  • Extensive-form game — An extensive form game is a specification of a game in game theory. This form represents the game as a tree. Each node (called a decision node) represents every possible state of play of the game as it is played. Play begins at a unique initial… …   Wikipedia

  • Normal-form game — In game theory, normal form is a way of describing a game. Unlike extensive form, normal form representations are not graphical per se, but rather represent the game by way of a matrix. While this approach can be of greater use in identifying… …   Wikipedia

  • normal form game — noun Formally, a structure where P = 1,2, ...,m is a set of players, is an m tuple of pure strategy sets, one for each player, and is an m tuple of payoff functions. <! If someone can turn the math to inline math, please do it. See Also:… …   Wiktionary

  • Game theory — is a branch of applied mathematics that is used in the social sciences (most notably economics), biology, engineering, political science, computer science (mainly for artificial intelligence), and philosophy. Game theory attempts to… …   Wikipedia

  • Game tree — If you re looking for game tree as it s used in game theory (not combinatorial game theory), please see Extensive form game. In game theory, a game tree is a directed graph whose nodes are positions in a game and whose edges are moves. The… …   Wikipedia

  • 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

  • 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

  • Combinatorial game theory — This article is about the theory of combinatorial games. For the theory that includes games of chance and games of imperfect knowledge, see Game theory. Mathematicians playing Konane at a Combinatorial game theory workshop (for technical content …   Wikipedia

  • Sequential game — In game theory, a sequential game is a game where one player chooses his action before the others choose theirs. Importantly, the later players must have some information of the first s choice, otherwise the difference in time would have no… …   Wikipedia

  • Cooperative game — This article is about a part of game theory. For video gaming, see Cooperative gameplay. For the similar feature in some board games, see cooperative board game In game theory, a cooperative game is a game where groups of players ( coalitions )… …   Wikipedia

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