Approximating pure nash equilibrium in cut, party affiliation, and satisfiability games

Abstract

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 PLS-complete. 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.