Hotelling Games on Networks: Efficiency of Equilibria

Gaëtan Fournier and Marco Scarsini

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We consider a Hotelling game where a finite number of retailers choose a location, given that their potential customers 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 bore 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 term of the induced price of anarchy, i.e., the ratio of the worst equilibrium cost and the optimal cost, and the induced 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 two and one, respectively.

Keywords: Induced price of anarchy; induced price of stability; location games on networks; pure equilibria; large games; Prix de l'anarchie induit; prix de la stabilité induit; jeu de location sur un réseau; équilibre pur (search for similar items in EconPapers)
Date: 2014-04
New Economics Papers: this item is included in nep-com, nep-hpe, nep-ind, nep-net and nep-sea
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00983085v1
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Citations: View citations in EconPapers (5)

Published in 2014

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Related works:
Working Paper: Hotelling Games on Networks: Efficiency of Equilibria (2014)
Working Paper: Hotelling Games on Networks: Efficiency of Equilibria (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-00983085

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