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In game theory, an extensive-form game is a specification of a game allowing 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 game outcomes.
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 ...
This equivalence, notably formalized in Kuhn's theorem, simplifies the analysis of such games. [4] It is a core component of how game theorists analyze extensive-form games. The formal definition of perfect recall involves the concept of information sets in extensive-form games. It ensures that if a player reaches a certain information set, the ...
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 ...
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 ...
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;