Bern Sturmfels
UC at Berkeley
Abstract
We present an algebraic approach to Nash equilibria in game theory, along the lines of Chapter 6 in my new book
"Solving Systems of Polynomial Equations" (http://math.berkeley.edu/~bernd/cbms.html). 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.