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2017 | OriginalPaper | Chapter

Large Spatial Competition

Authors : Matías Núñez, Marco Scarsini

Published in: Spatial Interaction Models

Publisher: Springer International Publishing

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Abstract

We consider spatial competition when consumers are arbitrarily distributed on a compact metric space. Retailers can choose one of finitely many locations in this space. We focus on symmetric mixed equilibria which exist for any number of retailers. We prove that the distribution of retailers tends to agree with the distribution of the consumers when the number of competitors is large enough. The results are shown to be robust to the introduction of (1) randomness in the number of retailers and (2) different ability of the retailers to attract consumers.

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previous chapter An Equilibrium-Econometric Analysis of Rental Housing Markets with Indivisibilities

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There are several real-life applications where the strategic behavior of the retailers is subject to feasibility constraints as, for instance, when zoning regulations are enforced. Land use regulation has been extensively analyzed in urban economics, mostly from an applied perspective. It is often argued that zoning can have anti-competitive effects and at the same time be beneficial since it might solve problems of externalities [see 31, for a recent work on this area].

Throughout, we assume that competition among retailers is only in terms of location, not price. We do this for several reasons. First, there exist several markets where price is not decided by retailers: think, for instance of newsvendors, shops operating under franchising, pharmacies in many countries, etc. Second, our model without pricing can be used to study other topics, e.g., political competition, when candidates have to take position on several, possibly related, issues. Finally several of the existing models that allow competition on location and pricing are two-stage models, where competition first happens on location and subsequently on price. Our game could be seen as a model of the first stage. It is interesting to notice that the recent paper by Heijnen and Soetevent [16] deals with the second stage in a location model on a graph, assuming that the first has already been solved.

Two main possibilities have been explored to solve for this lack of equilibrium: either alternative candidates’ objectives were considered (as in [6]) or the use of mixed strategies (as in [4]).

Formally, [26] prove that the symmetric equilibrium strategies satisfy the claim assuming that the consumers are distributed in the interval [0,1] according to any twice continuously differentiable distribution function.

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Title: Large Spatial Competition
Authors: Matías Núñez
Marco Scarsini
Publisher: Springer International Publishing
Book: Spatial Interaction Models
Print ISBN: 978-3-319-52653-9

Electronic ISBN: 978-3-319-52654-6

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-52654-6_10

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