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Backward induction
A reasoning process in which players, working backward from the last possible moves in a game, anticipate each otherŐs rational choices.
Chicken
A two-person variable-sum symmetric game in which each player has two strategies: to swerve to avoid a collision, or not to swerve and cause a collision if the opponent has not swerved; Neither player has a dominant strategy; the compromise outcome, in which both players swerve, is not a Nash equilibrium, but the two outcomes in which one player swerves and the other does not are Nash equilibria.
Constant-sum game
A game in which the sum of payoffs to the players at each outcome is a constant, which can be converted to a zero-sum game by an appropriate change in the payoffs to the players that does not alter the strategic nature of the game.
Deception strategy
A player's announcement of a false preference to induce other players to choose strategies favorable to the deceiver.
Dominant strategy
A strategy that is sometimes better and never worse for a player than every other strategy, whatever strategies the other players choose.
Dominated strategy
A strategy that is sometimes worse and never better for a player than some other strategy, whatever strategies the other players choose.
Fair game
A zero-sum game is fair when the (expected) value of the game, obtained by using optimal strategies (pure or mixed), is zero.
Game tree
A symbolic tree, based on the rules of play in a game, in which the vertices, or nodes, of the tree represent choice points, and the branches represent alternative courses of action that the players can select.
Maximin
In a two-person zero-sum game, the largest of the minimum payoffs in each row of a payoff matrix.
Maximin strategy
In a two-person zero-sum game, the pure strategy of the row player corresponding to the maximin in a payoff matrix.
Minimax
In a two-person zero-sum game, the smallest of the maximum payoffs in each column of a payoff matrix.
Minimax strategy
In a two-person zero-sum game, the pure strategy of the column player corresponding to the minimax in a payoff matrix.
Minimax theorem
The fundamental theorem for two-person constant-sum games, stating that there always exist optimal pure or mixed strategies that enable the two players to guarantee the value of the game.
Mixed strategy
A strategy that involves the random choice of pure strategies, according to particular probabilities; A mixed strategy of a player is optimal if it guarantees the value of the game.
Nash equilibrium
Strategies associated with an outcome such that no player can benefit by choosing a different strategy, given that the other players do not depart from their strategies.
Nonsymmetrical game
A two-person constant-sum game in which the row playerŐs gains are different from the column playerŐs gains, except when there is a tie.
Ordinal game
A game in which the players rank the outcomes from best to worst.
Paradox of the chair's position
This paradox occurs when being chair (with a tie-breaking vote) hurts rather than helps the chair if voting is sophisticated.