game matrix

An m×n matrix which gives the possible outcome of a two-person zero-sum game when player A has m possible moves and player B n moves. The analysis of the matrix in order to determine optimal strategies is the aim of game theory. The so-called "augmented" payoff matrix is defined as follows: G = [ | P_0 | P_1 | P_2 | ... | P_n | P_(n + 1) | P_(n + 2) | ... | P_(n + m) | 0 | 1 | 1 | ... | 0 | 0 | 0 | ... | 0 | -1 | a_11 | a_12 | ... | a_(1n) | 1 | 0 | ... | 0 | -1 | a_21 | a_22 | ... | a_(2n) | 0 | 1 | ... | 0 | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ | -1 | a_(m1) | a_(m2) | ... | a_(m n) | 0 | 0 | ... | 1].

augmented matrix | game theory | zero-sum game