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A zero-sum game is also called a strictly competitive game, while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, [5] or with Nash equilibrium. Prisoner's Dilemma is a classic non-zero-sum game. [6]
In the mathematical theory of games, in particular the study of zero-sum continuous games, not every game has a minimax value. This is the expected value to one of the players when both play a perfect strategy (which is to choose from a particular PDF). This article gives an example of a zero-sum game that has no value. It is due to Sion and ...
These are zero-sum games with very high payoffs, and the players have devoted their lives to become experts. Often such games are strategically similar to matching pennies: In soccer penalty kicks , the kicker has two options – kick left or kick right – and the goalie has two options – jump left or jump right. [ 11 ]
A veto denotes the ability (or right) of some player to prevent a specific alternative from being the outcome of the game. A player who has that ability is called a veto player. Antonym: Dummy. Weakly acceptable game is a game that has pure nash equilibria some of which are pareto efficient. Zero sum game
Solution of zero-sum simple pursuit games such as "lifeline game", "two pursuers – one evader game", "deadline game in a half plane". Proof of the existence of an epsilon-saddle point in piecewise open loop strategies in general dynamic zero-sum games with prescribed duration and independent motions. Method of solution of pursuit games based ...
In game theory, Silverman's game is a two-person zero-sum game played on the unit square. It is named for mathematician David Silverman. It is played by two players on a given set S of positive real numbers. Before play starts, a threshold T and penalty ν are chosen with 1 < T < ∞ and 0 < ν < ∞.
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If the nim-sum is zero, then the next player will lose if the other player does not make a mistake. To find out which move to make, let X be the nim-sum of all the heap sizes. Find a heap where the nim-sum of X and heap-size is less than the heap-size; the winning strategy is to play in such a heap, reducing that heap to the nim-sum of its ...