A game in which a matrix contains numerical data giving information about what happens according to the strategies chosen by two opponents or players. By convention, the matrix [a_ij] gives the payoff to one of the players, R: when R chooses the ith row and the other player, C, chooses the jth column, then C pays to R an amount of a_ij units. (If a_ij is negative, then in fact R pays C a certain amount.) This is an example of a zero‐sum game because the total amount received by the two players is zero: R receives a_ij units and C receives −a_ij units.

If the game is a strictly determined game, and R and C use conservative strategies, C will always pay R a certain amount, which is the value of the game. If the game is not strictly determined, then by the Fundamental Theorem of Game Theory, there is again a value for the game, being the expectation when R and C use mixed strategies that are optimal.