Title: Hard-to-Solve Bimatrix Games
Speaker: Prof. Bernhard von Stengel
Affiliation: Depatment of Mathematics – London School of Economics and Political Science
Location: CPSE seminar room (C615 Roderic Hill)
Time: 2:00pm

Abstract. A bimatrix game is a two-player game in strategic form, a basic model in game theory. A Nash equilibrium is a pair of (possibly randomized) strategies, one for each player, so that no player can do better by unilaterally changing his or her strategy. In this talk, which will introduce the main concepts and geometric tools, we show that the commonly used Lemke-Howson algorithm for finding one equilibrium of a bimatrix game is exponential. The algorithm is a pivoting method similar to the simplex algorithm for linear programming. We present a class of square bimatrix games for which the shortest Lemke-Howson path grows exponentially in the dimension d of the game. We construct the games using pairs of dual cyclic polytopes with 2d facets in d-space. The paths are recursively composed so that their lengths grow like Fibonacci numbers. We also mention subsequent results and open problems in the area.

About the speaker. Diploma in Mathematics from Aachen, MSc in Computer Sciences at Austin/Texas (student of Edsger W. Dijkstra), PhD in Passau, Habilitation in Munich, Postdoc at Berkeley, Tilburg and ETH Zurich (with a Heisenberg grant), at LSE Mathematics since 1998. Interested in algorithmic game theory longer than the research area has that name.