## Two-Person Zero-Sum Games and the Minimax Theorem |

**Julius Barbanel**

Union College

May 27, 1998

5:00 pm

Bailey Hall 201

Refreshments at 4:45

Math Department Common Room

Two-person games model situations in which there are two players, each with some finite list of strategies from which one strategy must be chosen. A play of the game consists of a choice of strategy by each player. For each possible pair of strategy choices by the two players, payoffs (a sum paid to or collected from each player) are assigned. A game is "zero-sum" if, for each possible play of the game, one player's gain precisely equals the other player's loss.We shall consider various aspects of two-person zero-sum games. How should a player decide on the best strategy to pick? If the game is repeated many times, why does it make more sense to use "mixed strategies" than to always pick the same strategy? How can players decide on the best way of mixing strategies? We conclude with a central and remarkable result called the Minimax Theorem.

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