An 
matrix
which gives the possible outcome of a two-person zero-sum
game when player A has 
possible moves and player B 
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].](/images/equations/PayoffMatrix/NumberedEquation1.svg) |
