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Location Games on Networks: Existence and Efficiency of Equilibria

2018; Institute for Operations Research and the Management Sciences; Linguagem: Inglês

10.1287/moor.2017.0921

1526-5471

Gaëtan Fournier, Marco Scarsini,

Game Theory and Voting Systems

AboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Go to Section HomeMathematics of Operations ResearchVol. 44, No. 1 Location Games on Networks: Existence and Efficiency of EquilibriaGaëtan Fournier , Marco Scarsini Gaëtan Fournier , Marco Scarsini Published Online:1 Aug 2018https://doi.org/10.1287/moor.2017.0921AbstractWe consider a game where a finite number of retailers choose a location, given that their potential consumers are distributed on a network. Retailers do not compete on price but only on location, therefore each consumer shops at the closest store. We show that when the number of retailers is large enough, the game admits a pure Nash equilibrium and we construct it. We then compare the equilibrium cost borne by the consumers with the cost that could be achieved if the retailers followed the dictate of a benevolent planner. We perform this comparison in terms of the Price of Anarchy (i.e., the ratio of the worst equilibrium cost and the optimal cost) and the Price of Stability (i.e., the ratio of the best equilibrium cost and the optimal cost). We show that, asymptotically in the number of retailers, these ratios are bounded by two and one, respectively. Previous Back to Top Next FiguresReferencesRelatedInformationCited byThe Buck-Passing GameRoberto Cominetti, Matteo Quattropani, Marco Scarsini8 November 2021 | Mathematics of Operations Research, Vol. 47, No. 3General distribution of consumers in pure Hotelling games14 November 2018 | International Journal of Game Theory, Vol. 48, No. 1 Volume 44, Issue 1February 2019Pages 1-375, C2 Article Information Metrics Information Received:January 19, 2016Accepted:November 28, 2017Published Online:August 01, 2018 Copyright © 2018, INFORMSCite asGaëtan Fournier, Marco Scarsini (2018) Location Games on Networks: Existence and Efficiency of Equilibria. Mathematics of Operations Research 44(1):212-235. https://doi.org/10.1287/moor.2017.0921 KeywordsPrice of AnarchyPrice of Stabilitylocation games on networksHotelling gamespure equilibrialarge gamesPDF download