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The game must satisfy the following criteria: there are two players in the game; the game is of perfect information; the board game is finite; the two players can take alternate turns; and there is no chance element present. Zermelo has stated that there are many games of this type; however his theorem has been applied mostly to the game chess.
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 ...
Chess initial position. The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. [1] There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame.
A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which results in multiple pure strategy Nash equilibria in which players choose matching strategies ...
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.
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 ...
The first game is simply sequential―when player 2 makes a choice, both parties are already aware of whether player 1 has chosen O(pera) or F(ootball). The second game is also sequential, but the dotted line shows player 2's information set. This is the common way to show that when player 2 moves, he or she is not aware of what player 1 did.
Sequential games with perfect information—where all prior moves are known—can be analyzed using combinatorial game theory, a mathematical approach to strategic decision-making. In such games, a subgame perfect equilibrium can be determined through backward induction , a process of working from the end of the game back to the start to ...