Competing over a finite number of locations
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We consider a Hotelling location game where retailers can choose one of a finite number of locations. Consumers have strict preferences over the possible available store locations and retailers aim to attract the maximum number of consumers. We prove that a pure strategy equilibrium exists if the number of retailers is large enough. Moreover, as the number of retailers grows large, in equilibrium the distribution of retailers over the locations converges to the distribution of consumers’ preferences.
KeywordsHotelling games Pure equilibria Large games Political competition
JEL ClassificationC72 D72 R30 R39
The authors thank Clémence Christin, Fabian Gouret, and Giacomo Nannicini for their useful remarks and suggestions. The work of Matías Núñez is supported by the center of excellence MME-DII (ANR-11-LBX-0023-01). The work of Marco Scarsini is partially supported by PRIN 20103S5RN3 and MOE2013-T2-1-158. This author is a member of GNAMPA-INdAM.
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