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

Author

Listed:
  • Angelo Fanelli

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, C2I - Centre for Computational Intelligence [Nanyang] - Nanyang Technological University [Singapour])

  • Michele Flammini

    (GSSI - Gran Sasso Science Institute, DISIM - Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila] - UNIVAQ - Università degli Studi dell'Aquila = University of L'Aquila)

  • Luca Moscardelli

    (Dipartimento di Scienze - Universita di Chieti-Pescara - UNICH - Universita' degli Studi "G. d'Annunzio" Chieti-Pescara)

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.

Suggested Citation

  • Angelo Fanelli & Michele Flammini & Luca Moscardelli, 2012. "The speed of convergence in congestion games under best-response dynamics," Post-Print halshs-02094392, HAL.
    • Handle: RePEc:hal:journl:halshs-02094392
    DOI: 10.1145/2229163.2229169
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    Cited by:

    1. Vittorio Bilò & Mauro Paladini, 2016. "On the performance of mildly greedy players in cut games," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1036-1051, November.
    2. Hoang, Lê Nguyên & Soumis, François & Zaccour, Georges, 2019. "The return function: A new computable perspective on Bayesian–Nash equilibria," European Journal of Operational Research, Elsevier, vol. 279(2), pages 471-485.

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