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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 ...
Backgammon includes chance events, but by some definitions is classified as a game of perfect information. Poker is a game of imperfect information, as players do not know the private cards of their opponents. 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 ...
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 ...
An abstract strategy game is a board, card or other game where game play does not simulate a real world theme, and a player's decisions affect the outcome.Many abstract strategy games are also combinatorial, i.e. they provide perfect information, and rely on neither physical dexterity nor random elements such as rolling dice or drawing cards or tiles.
Figure 1: A game tree which depicts each player's possible information set by showing the options at each vertex (A and B for player's 1 and 2 respectively) Information sets are used in extensive form games and are often depicted in game trees. Game trees show the path from the start of a game and the subsequent paths that can be made depending ...
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;
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 ...
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 ...