Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Simple local search problems that are hard to solve
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STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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Market sharing games applied to content distribution in ad-hoc networks
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The complexity of pure Nash equilibria
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The Price of Stability for Network Design with Fair Cost Allocation
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The Price of Routing Unsplittable Flow
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The price of anarchy of finite congestion games
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The complexity of computing a Nash equilibrium
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Settling the Complexity of Two-Player Nash Equilibrium
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On the Impact of Combinatorial Structure on Congestion Games
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Approximation algorithms for distributed and selfish agents
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On the convergence of multicast games in directed networks
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Convergence to approximate Nash equilibria in congestion games
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Inapproximability of pure nash equilibria
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The Speed of Convergence in Congestion Games under Best-Response Dynamics
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Convergence and approximation in potential games
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Efficient coordination mechanisms for unrelated machine scheduling
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Intrinsic robustness of the price of anarchy
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Concurrent imitation dynamics in congestion games
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Convergence and approximation in potential games
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We study the speed of convergence of decentralized dynamics to approximately optimal solutions in potential games. We consider α-Nash dynamics in which a player makes a move if the improvement in his payoff is more than an α factor of his own payoff. Despite the known polynomial convergence of α-Nash dynamics to approximate Nash equilibria in symmetric congestion games [7], it has been shown that the convergence time to approximate Nash equilibria in asymmetric congestion games is exponential [25]. In contrast to this negative result, and as the main result of this paper, we show that for asymmetric congestion games with linear and polynomial delay functions, the convergence time of α-Nash dynamics to an approximate optimal solution is polynomial in the number of players, with approximation ratio that is arbitrarily close to the price of anarchy of the game. In particular, we show this polynomial convergence under the minimal liveness assumption that each player gets at least one chance to move in every T steps. We also prove that the same polynomial convergence result does not hold for (exact) best-response dynamics, showing the α-Nash dynamics is required. We extend these results for congestion games to other potential games including weighted congestion games with linear delay functions, cut games (also called party affiliation games) and market sharing games.