Minimax Theorem

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  and  be mixed strategies for players A and B. Let  be the payoff matrix. Then

where  is called the value of the game and  and  are called the solutions. It also turns out that if there is more than one optimal mixed strategy, there are infinitely many.

In the Season 4 opening episode "Trust Metric" (2007) of the television crime drama NUMB3RS, math genius Charlie Eppes mentions that he used the minimax theorem in an attempt to derive an equation describing friendship.

REFERENCES:

Willem, M. Minimax Theorem. Boston, MA: Birkhäuser, 1996.