On Cournot oligopolies with a biconcave price function

Pierre von Mouche

doi:10.3934/jdg.2025005

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2026, Volume 14: 1-17. Doi: 10.3934/jdg.2025005

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On Cournot oligopolies with a biconcave price function

Pierre von Mouche^,

Wageningen University, Wageningen, The Netherlands, Corvinus Institute of Advanced Studies, Budapest, Hungary

^*Corresponding author: Pierre von Mouche
^*Corresponding author: Pierre von Mouche

The author thanks the late Prof. Ferenc Szidarovszky for various comments on a first version of the article.

Received: November 2024

Revised: March 2025

Early access: April 2025

Published online: April 2025

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Abstract

The power of a recent result for Nash equilibria of sum-aggregative games is illustrated by providing a variant of Ewerhart's equilibrium uniqueness theorem for Cournot oligopolies with a biconcave essential price function. This variant, contrary to the original result, allows for industry revenue that is discontinuous at 0 and can be considered a major generalization of the classical uniqueness result of Szidarovszky and Okuguchi for rent-seeking games. It assumes that the elasticity of the price function has a limit when its argument tends to zero.

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Mathematics Subject Classification: 91B54, 52A01.

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References

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