Payoff Matrix

An $m\times n$ 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:

$${\hbox{\sf G}}=\!\left[{\matrix{ & P_0 & P_1 & P_2 & \cdots... ...} & a_{m2} & \cdots & a_{mn} & 0 & 0 & \cdots & 1\cr}}\right].$$

See also Game Theory, Zero-Sum Game