The efficiency of best-response dynamics

Michal Feldman, Yuval Snappir, Tami Tamir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationAlgorithmic Game Theory - 10th International Symposium, SAGT 2017, Proceedings
EditorsVittorio Bilo, Michele Flammini
PublisherSpringer Verlag
Pages186-198
Number of pages13
ISBN (Print)9783319666990
DOIs
StatePublished - 2017
Event10th International Symposium on Algorithmic Game Theory, SAGT 2017 - L’Aquila, Italy
Duration: 12 Sep 201714 Sep 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10504 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Symposium on Algorithmic Game Theory, SAGT 2017
Country/TerritoryItaly
CityL’Aquila
Period12/09/1714/09/17

Keywords

  • Best-response dynamics
  • Congestion games
  • Deviator rules
  • Price of anarchy

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