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Payoff 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_(mn) 0 0 ... 1].

See also

Augmented Matrix, Game Theory, Zero-Sum Game

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Cite this as:

Weisstein, Eric W. "Payoff Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PayoffMatrix.html

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