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(of a matrix game)

Suppose that, in the matrix game given by the m×n matrix [aij], the mixed strategies x and y for the two players are given by x=(x1, x2,…, xm), and y=(y1, y2,…, yn). The expectation E(x, y) is given byIf A=[aij], and x and y are written as column matrices, E(x, y)=xTAy. The expectation can be said, loosely, to give the average payoff each time when the game is played many times with the two players using these mixed strategies.

Subjects: Mathematics.

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