Equilibrium Computation

Summary

The focus of this seminar was the algorithmic problem of computing equilibria in games and market models, viewed from both the theoretical and practical perspective. The equilibrium computation problem is one of the central topics in the rapidly expanding field of algorithmic game theory.

The seminar was a follow-up to Seminar 07471, on the same topic, but with three new organizers, and with a focus on some of the aspects of this problem that received relatively little attention in Seminar 07471. One of the major themes of this seminar was dynamics, i.e., exploring the agents' behavior (at both individual and collective level) that leads to the discovery of equilibria, and, more generally, adaptive changes in the collective behavior. Discussed were the classic game-theoretic approaches to this topic (organizer: von Stengel) as well as more recent computational and simulation-based techniques, as studied by the multi-agent community (organizer: Elkind). Another key emphasis was on algorithms and complexity results for market equilibria and their applications to Nash Bargaining Games (organizer: Vazirani). We also compared these approaches with computational and geometric aspects of the central Linear Complementarity Problem (LCP) in mathematical programming (organizer: Megiddo). Finally, since the last seminar there was significant progress understanding the complexity of important algorithms, such as strategy iteration, for solving two-player zero-sum games of infinite duration. Progress in this area has strong connections to mathematical programming and was discussed and extended (organizer: Miltersen).

The following abstracts indicate the diversity of topics and their rich interconnections that were explored during a very successful seminar.