“expectation(of a matrix game)”的概念、定义、翻译、参考文献-科学参考

expectation(of a matrix game)

Mathematics

Suppose that, in the matrix game given by the m × n matrix [a_ij], the mixed strategies x and y for the two players are given by x = (x₁, x₂,…, x_m), and y = (y₁, y₂,…, y_n). The expectation E(x,y) is given by

$E (x, y) = \sum_{i = 1}^{m} \sum_{j = 1}^{n} x_{i} a_{i j} y_{j} .$

If A = [a_ij], then E(x,y) = xAy^T. 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.

单词	expectation(of a matrix game)
释义	expectation(of a matrix game) Mathematics Suppose that, in the matrix game given by the m × n matrix [a_ij], the mixed strategies x and y for the two players are given by x = (x₁, x₂,…, x_m), and y = (y₁, y₂,…, y_n). The expectation E(x,y) is given by $E (x, y) = \sum_{i = 1}^{m} \sum_{j = 1}^{n} x_{i} a_{i j} y_{j} .$ If A = [a_ij], then E(x,y) = xAy^T. 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.
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