# Mathematics Colloquia and Seminars

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### Algebraic geometry of Nash equilibria

**Algebra & Discrete Mathematics**

Speaker: | Prof. Bernd Sturmfels, UC Berkeley |

Location: | 693 Kerr |

Start time: | Thu, Nov 14 2002, 12:10PM |

We present an algebraic approach to Nash equilibria in game theory. The set of all Nash equilibria of an N-person game is a real algebraic variety, which is typically a finite set. A combinatorial formula for its expected cardinality was given by the economists McKelvey and McLennan in 1997. We show how to find all Nash equilibria using computational algebraic geometry, and we present the Universality Theorem (proved by Ruchira Datta in 2002) which states that every real algebraic variety arises from a game with three players.