Approximating pure nash equilibrium in cut, party affiliation, and satisfiability 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 > 0, we design an algorithm to compute in polynomial time a (3 + )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 pa...

• Type: Conference
• Year: 2010
• Where: SIGECOM
• Authors: Anand Bhalgat, Tanmoy Chakraborty, Sanjeev Khanna
• Keywords: ECommerce, Party Affiliation Games, Potential Games, Pure Nash Equilibrium, SIGECOM 2010