A payoff matrix, or payoff table, is a simple chart used in basic game theory situations to analyze and evaluate a situation in which two parties have a decision to make. The matrix is typically a two-by-two matrix with each square divided in half, with one half for each person involved.
The payoff matrix is organized with the first person's choices along the top and the second person's choices along the side. All possible results are filled in the matrix, which is why the situation must be one with limited choices for each person. Each of the possible results can be evaluated to determine what is the optimal choice for each person involved.