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Zermelo's theorem can be applied to all finite-stage two-player games with complete information and alternating moves. 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.
This game is finite, and the total number of moves (and thus the game's winner) is predetermined by the initial number of crosses: the players cannot affect the result by their play. Thus, this variant may be termed, after Conway's categorisation of mathematics itself, a "one player game". Each move removes two free ends and introduces two more.
In the star game, the only valid move leads to the zero game, which means that whoever's turn comes up during the star game automatically wins. An additional type of game, not found in Domineering, is a loopy game, in which a valid move of either left or right is a game that can then lead back to the first game.
Determined game (or Strictly determined game) In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies. [2] [3] Dictator A player is a strong dictator if he can guarantee any outcome regardless of the other players.
An imperfect information game is played when the players do not know all moves already made by the opponent such as a simultaneous move game. [22] 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]
In economics and game theory, the decisions of two or more players are called strategic complements if they mutually reinforce one another, and they are called strategic substitutes if they mutually offset one another. These terms were originally coined by Bulow, Geanakoplos, and Klemperer (1985).
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A finite game (sometimes called a founded game [1] or a well-founded game [2]) is a two-player game which is assured to end after a finite number of moves. Finite games may have an infinite number of possibilities or even an unbounded number of moves, so long as they are guaranteed to end in a finite number of turns.