Existence and uniqueness of price equilibria in location-based models of differentiation with full coverage

Janko Hernández Cortés () and Paolo Morganti ()
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Janko Hernández Cortés: Departament of Business Administration. ITAM.
Paolo Morganti: Universidad Panamericana Facultad de Ciencias Económicas y Empresariales.

Journal of Economics, 2022, vol. 136, issue 2, No 2, 115-148

Abstract: Abstract In location-based models of price competition, traditional sufficient conditions for existence and uniqueness of an equilibrium (Caplin and Nalebuff in Econometrica 59(1):25–59) are not robust for the firm that serves the right-tail of the consumers’ distribution. Interestingly, as we relax these conditions, we observe only two new alternative cases. Moreover, we identify a novel, easily testable condition for uniqueness that is weaker than log-concavity and that can also apply to Mechanism Design. Thanks to this general framework, we can solve the equilibrium of general vertical differentiation models numerically and show that inequality has a U-shaped effect on profits and prices of a high-quality firm. Moreover, we prove that extreme levels of concentration can dissolve natural monopolies and restore competition, contrary to the Uniform case.

Keywords: Price Competition; Product Positioning; Vertical Differentiation; Dispersion; Discontinuous Games; Existence of Equilibria; C72; D43; L13 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:kap:jeczfn:v:136:y:2022:i:2:d:10.1007_s00712-021-00770-8

DOI: 10.1007/s00712-021-00770-8

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