Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
On finding and verifying locally optimal solutions
SIAM Journal on Computing
Simple local search problems that are hard to solve
SIAM Journal on Computing
Integer Linear Programs and Local Search for Max-Cut
SIAM Journal on Computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Market sharing games applied to content distribution in ad-hoc networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
Improved equilibria via public service advertising
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Nash Dynamics in Congestion Games with Similar Resources
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Computing stable outcomes in hedonic games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Computing stable outcomes in hedonic games with voting-based deviations
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
On allocations with negative externalities
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Proceedings of the 13th ACM Conference on Electronic Commerce
Dynamics of profit-sharing games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Decentralized dynamics for finite opinion games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
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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. 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.