Approximating Pure Nash Equilibrium in Cut, Party Affiliation, and Satisfying Games

Cut games and party affiliation games are well-known classes of potential games. Schaffer and Yannakakis showed that computing pure Nash equilibrium in these games is PLScomplete. In general potential games, even the problem of computing any finite approximation to a pure equilibrium is also PLS-complete. We show that for any є > 0, we design an algorithm to compute in polynomial time a (3 + є)approximate pure Nash equilibrium for cut and party affiliation games. Prior to our work, only a trivial polynomial factor approximation was known for these games. Our approach extends beyond cut and party affiliation games to a more general class of satisfiability games. A key idea in our approach is a pre-processing phase that creates a partial order on the players. We then apply Nash dynamics to a sequence of restricted games derived from this partial order. We show that this process converges in polynomial-time to an approximate Nash equilibrium by strongly utilizing the properties of the partial order. This is in strong contrast to earlier results for some other classes of potential games that compute an approximate equilibrium by a direct application of Nash dynamics on the original game. In fact, we also show that such a technique cannot yield FPTAS for computing equilibria in cut and party affiliation games. Disciplines Computer Sciences Comments Bhalgat, A., Chakraborty, T., & Khanna, S., Approximating Pure Nash Equilibrium in Cut, Party Affiliation, and Satisfiability Games, 11th ACM Conference on Electronic Commerce, June 2011, doi: 10.1145/ 1807342.1807353 ACM COPYRIGHT NOTICE. Copyright © 2011 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications Dept., ACM, Inc., fax +1 (212) 869-0481, or [email protected]. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/cis_papers/667 Approximating Pure Nash Equilibrium in Cut, Party Affiliation, and Satisfiability Games