Existence and uniqueness of price equilibria in location-based models of differentiation with full coverage
Journal
Journal of Economics
ISSN
0931-8658
1617-7134
Date Issued
2022
Author(s)
Hernández Cortés, Janko
Type
Resource Types::text::journal::journal article
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.
How to cite
Cortés, J. H., & Morganti, P. (2022). Existence and uniqueness of price equilibria in location-based models of differentiation with full coverage. Journal of Economics 136, 115–148 (2022). https://doi.org/10.1007/s00712-021-00770-8