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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 ...
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 ...
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 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 ...
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 on each player's next move. For non-perfect information game problems, there is hidden information.
An extensive-form game with incomplete information is presented below in Figure 2. Note that the node for Player 1 with actions A and B, and all succeeding actions is a subgame. Player 2's nodes are not a subgame as they are part of the same information set. Figure 2
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.
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;