matrix game

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A game in which a matrix contains numerical data giving information about what happens according to the strategies chosen by two opponents or players. By convention, the matrix [aij] gives the pay-off to one of the players, R: when R chooses the i-th row and the other player, C, chooses the j-th column, then C pays to R an amount of aij units. (If aij is negative, then in fact R pays C a certain amount.) This is an example of a zero-sum game because the total amount received by the two players is zero: R receives aij units and C receives −aij units.

If the game is a strictly determined game, and R and C use conservative strategies, C will always pay R a certain amount, which is the value of the game. If the game is not strictly determined, then by the Fundamental Theorem of Game Theory, there is again a value for the game, being the expectation (loosely, the average payoff each time when the game is played many times) when R and C use mixed strategies that are optimal.

Subjects: Mathematics.

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