Hotelling Games on Networks: Existence and Efficiency of Equilibria

61 Pages Posted: 12 Apr 2014 Last revised: 25 Jan 2016

See all articles by Gaëtan Fournier

Gaëtan Fournier

Tel Aviv University - School of Mathematical Sciences

Marco Scarsini

LUISS, Dipartimento di Economia e Finanza

Date Written: January 18, 2016

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, utility games.

JEL Classification: C72, R30, R39

Suggested Citation

Fournier, Gaëtan and Scarsini, Marco, Hotelling Games on Networks: Existence and Efficiency of Equilibria (January 18, 2016). Available at SSRN: https://ssrn.com/abstract=2423345 or http://dx.doi.org/10.2139/ssrn.2423345

Gaëtan Fournier

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Marco Scarsini (Contact Author)

LUISS, Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

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