Events - Colloquia & Seminars

CCIS Colloquium Fall 2006

On the Computation and Approximation of Two-Player Nash Equilibria

Speaker: Xi Chen

Affiliation: Tsinghua University

Date: Wednesday, December 13, 2006

Talk: 12:00 pm, 110 WVH

Abstract

In 1950, Nash showed that every non-cooperative game has an equilibrium. Before his work, the result was known only for two-player zero-sum games. While von Neumann's minimax theorem was the mathematical foundation of the two-player zero-sum game, Brouwer's and Katutani's fixed point theorems were crucially used in Nash's proofs. His approach was later used by Arrow and Debreu in their development of the general equilibrium theory.

Fourteen years after Nash's work, Lemke and Howson designed a simplex-like path-following algorithm for finding a Nash equilibrium in a general two-player game. Despite its several appealing properties, this algorithm was recently shown to have exponential worst-case complexity. In contrast, in his groundbreaking work, Khachiyan showed that the ellipsoid algorithm can solve any linear program and hence any two-player zero-sum game in polynomial time. His success, however, has not been extended to general two-player games --- no polynomial-time algorithm has yet been found for this remarkable problem.

In this talk, Xi will present the recent results in characterizing the complexity of computing and approximating two-player Nash equilibria.

Biography

Xi Chen is a fourth-year PhD student in the department of Computer Science at Tsinghua University. Xi Chen studied in the Physics department of Tsinghua University and received B.S. there in 2003.

Xi's research interests lie in the area of Theoretical Computer Science. Xi is particularly interested in the computational complexity of natural problems in Algorithmic Game Theory and Computational Biology.