The fundamental theorem of game theory which states that every finite, zero-sum, two-person game has optimal mixed strategies. It was proved by John von Neumann in 1928. Formally, let X and Y be mixed strategies for players A and B. Let A be the payoff matrix. Then max_X min_Y X^T A Y = min_Y max_X X^T A Y = v, where v is called the value of the game and X and Y are called the solutions. It also turns out that if there is more than one optimal mixed strategy, there are infinitely many.

game | game theory | mixed strategy