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In game theory, an extensive-form game is a specification of a game allowing (as the name suggests) for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible ...
Perfect information: A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceded them. Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if ...
Examples of games with incomplete but perfect information are conceptually more difficult to imagine, such as a Bayesian game. A game of chess is a commonly given example to illustrate how the lack of certain information influences the game, without chess itself being such a game. One can readily observe all of the opponent's moves and viable ...
Examples of perfect-information games include tic-tac-toe, checkers, chess, and Go. [23] [24] [25] Many card games are games of imperfect information, such as poker and bridge. [26] Perfect information is often confused with complete information, which is a similar concept pertaining to the common knowledge of each player's sequence, strategies ...
Chess is an example of a game with perfect information, as each player can see all the pieces on the board at all times. [2] Other games with perfect information include tic-tac-toe, Reversi, checkers, and Go. [3] Academic literature has not produced consensus on a standard definition of perfect information which defines whether games with ...
Sequential games are governed by the time axis and represented in the form of decision trees. Sequential games with perfect information can be analysed mathematically using combinatorial game theory. Decision trees are the extensive form of dynamic games that provide information on the possible ways that a given game can be played.
Essentially, combinatorial game theory has contributed new methods for analyzing game trees, for example using surreal numbers, which are a subclass of all two-player perfect-information games. [3] The type of games studied by combinatorial game theory is also of interest in artificial intelligence, particularly for automated planning and ...
A perfect Bayesian equilibrium in an extensive form game is a combination of strategies and a specification of beliefs such that the following two conditions are satisfied: [15] Bayesian consistency: the beliefs are consistent with the strategies under consideration;