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We present an algorithm that computes approximate pure Nash equilibria in a broad class of constraint satisfaction games that generalize the well-known cut and party affiliation games. Our results improve previous ones by Bhalgat et al. (EC 10) in terms of the obtained approximation guarantee. More importantly, our algorithm identifies a polynomially-long sequence of improvement moves from any initial state to an approximate equilibrium in these games. The existence of such short sequences is an interesting structural property which, to the best of our knowledge, was not known before. Our techniques adapt and extend our previous work for congestion games (FOCS 11) but the current analysis is considerably simpler.

Short Sequences of Improvement Moves Lead to Approximate Equilibria in Constraint Satisfaction Games