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The speed of convergence in congestion games under best-response dynamics

Abstract : We investigate the speed of convergence of best response dynamics to approximately optimal solutions in congestion games with linear delay functions. In Ackermann et al. [2008] it has been shown that the convergence time of such dynamics to Nash equilibrium may be exponential in the number of players n. Motivated by such a negative result, we focus on the study of the states (not necessarily being equilibria) reached after a limited number of players' selfish moves, and we show that Θ(n log log n) best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every O(n) steps each player performs a constant (and nonnull) number of best responses. We show that such result is tight also for the simplest case of singleton congestion games.
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https://halshs.archives-ouvertes.fr/halshs-02094392
Contributor : Anne l'Azou <>
Submitted on : Tuesday, April 9, 2019 - 3:57:12 PM
Last modification on : Monday, October 19, 2020 - 8:26:03 PM

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Angelo Fanelli, Michele Flammini, Luca Moscardelli. The speed of convergence in congestion games under best-response dynamics. ACM Transactions on Algorithms, Association for Computing Machinery, 2012, 8 (3), pp.1-15. ⟨10.1145/2229163.2229169⟩. ⟨halshs-02094392⟩

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