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The Efficiency of Best-Response Dynamics

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Algorithmic Game Theory (SAGT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10504))

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Abstract

Best response (BR) dynamics is a natural method by which players proceed toward a pure Nash equilibrium via a local search method. The quality of the equilibrium reached may depend heavily on the order by which players are chosen to perform their best response moves. A deviator rule S is a method for selecting the next deviating player. We provide a measure for quantifying the performance of different deviator rules. The inefficiency of a deviator rule S with respect to an initial strategy profile p is the ratio between the social cost of the worst equilibrium reachable by S from p and the social cost of the best equilibrium reachable from p. The inefficiency of S is the maximum such ratio over all possible initial profiles. This inefficiency always lies between 1 and the price of anarchy.

We study the inefficiency of various deviator rules in network formation games and job scheduling games (both are congestion games, where BR dynamics always converges to a pure NE). For some classes of games, we compute optimal deviator rules. Furthermore, we define and study a new class of deviator rules, called local deviator rules. Such rules choose the next deviator as a function of a restricted set of parameters, and satisfy a natural independence condition called independence of irrelevant players. We present upper bounds on the inefficiency of some local deviator rules, and also show that for some classes of games, no local deviator rule can guarantee inefficiency lower than the price of anarchy.

This work was partially supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 337122.

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Notes

  1. 1.

    Note that the vectors \(\mathbf {v}\) and \(\mathbf {v'}\) may correspond to different sets of players.

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel-Aviv University, Tel Aviv, Israel

    Michal Feldman & Yuval Snappir

  2. School of Computer Science, The Interdisciplinary Center, Herzliya, Israel

    Tami Tamir

Authors
  1. Michal Feldman
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  2. Yuval Snappir
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  3. Tami Tamir
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Corresponding author

Correspondence to Yuval Snappir .

Editor information

Editors and Affiliations

  1. University of Salento, Lecce, Italy

    Vittorio Bilò

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

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Feldman, M., Snappir, Y., Tamir, T. (2017). The Efficiency of Best-Response Dynamics. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-66700-3_15

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