# Hotelling Games on Networks: Efficiency of Equilibria

Working paper

Series:

CES Working Papers

Publisher:

Centre d’Economie de la Sorbonne

Year:

2014

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.