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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 |
Description
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.