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Independent Lazy Better-Response Dynamics on Network Games

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Algorithms and Complexity (CIAC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11485))

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Abstract

We study an independent best-response dynamics on network games in which the nodes (players) decide to revise their strategies independently with some probability. We provide several bounds on the convergence time to an equilibrium as a function of this probability, the degree of the network, and the potential of the underlying games. These dynamics are somewhat more suitable for distributed environments than the classical better- and best-response dynamics where players revise their strategies “sequentially”, i.e., no two players revise their strategies simultaneously.

A full version of this work is available online at [27].

Supported by IRIF (CNRS UMR 8243) and Inria project-team GANG.

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Notes

  1. 1.

    In this work we consider only pure Nash equilibria, which are the equilibria that occur in certain games when each player chooses one strategy out of the available ones. Other equilibrium concepts are also studied, most notably the mixed Nash equilibrium, where each player chooses a probability distribution over the available strategies.

  2. 2.

    As we assume that strategy sets are finite, the potential function is defined by a finite set of values. Rescaling the potential function so that different values are at least 1 apart, and then truncating the values to integers allows to obtain an equivalent game (with same dynamics). Additionally shifting the values allows to obtain a non-negative potential function for that game.

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Acknowledgments

We thank Damien Regnault and Nicolas Schabanel for inspiring discussions on closely related problems, and an anonymous reviewer for pointing out the last open question. Part of this work has been done while the first author was at LIAFA, Université Paris Diderot, supported by the French ANR Project DISPLEXITY.

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Authors and Affiliations

  1. Department of Computer Science, ETH Zurich, Zurich, Switzerland

    Paolo Penna

  2. Inria – Université Paris Diderot, Paris, France

    Laurent Viennot

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  1. Paolo Penna
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  2. Laurent Viennot
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Correspondence to Paolo Penna .

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Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Penna, P., Viennot, L. (2019). Independent Lazy Better-Response Dynamics on Network Games. In: Heggernes, P. (eds) Algorithms and Complexity. CIAC 2019. Lecture Notes in Computer Science(), vol 11485. Springer, Cham. https://doi.org/10.1007/978-3-030-17402-6_29

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  • DOI: https://doi.org/10.1007/978-3-030-17402-6_29

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  • Publisher Name: Springer, Cham

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