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Cournot games with biconcave demand

Author

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  • Christian Ewerhart

Abstract

Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either "nearly linear" or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.

Suggested Citation

  • Christian Ewerhart, 2011. "Cournot games with biconcave demand," ECON - Working Papers 016, Department of Economics - University of Zurich, revised Jan 2014.
    • Handle: RePEc:zur:econwp:016
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    File URL: https://www.zora.uzh.ch/id/eprint/51520/8/econwp016.pdf
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    1. Shaban, Ibrahim Abdelfadeel & Chan, F.T.S. & Chung, S.H., 2021. "A novel model to manage air cargo disruptions caused by global catastrophes such as Covid-19," Journal of Air Transport Management, Elsevier, vol. 95(C).
    2. Aswin Kannan & Uday V. Shanbhag, 2019. "Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants," Computational Optimization and Applications, Springer, vol. 74(3), pages 779-820, December.
    3. Gaumont, Damien & Badra, Yassine & Kamburova, Detelina, 2023. "Market-dependent preferences, positive and negative network effects and welfare," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 143-154.
    4. Rabah Amir, 2018. "Special issue: supermodularity and monotone methods in economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 547-556, October.
    5. Aiyuan Tao & X. Henry Wang & Bill Z. Yang, 2018. "Duopoly models with a joint capacity constraint," Journal of Economics, Springer, vol. 125(2), pages 159-172, October.
    6. Amir, Rabah & De Castro, Luciano & Koutsougeras, Leonidas, 2014. "Free entry versus socially optimal entry," Journal of Economic Theory, Elsevier, vol. 154(C), pages 112-125.
    7. Pierre von Mouche & Federico Quartieri, 2015. "Cournot Equilibrium Uniqueness in Case of Concave Industry Revenue: a Simple Proof," Economics Bulletin, AccessEcon, vol. 35(2), pages 1299-1305.
    8. Alós-Ferrer, Carlos & Buckenmaier, Johannes, 2017. "Cournot vs. Walras: A reappraisal through simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 257-272.
    9. Achim Hagen & Pierre von Mouche & Hans-Peter Weikard, 2020. "The Two-Stage Game Approach to Coalition Formation: Where We Stand and Ways to Go," Games, MDPI, vol. 11(1), pages 1-31, January.
    10. Tamás L. Balogh & Christian Ewerhart, 2015. "On the origin of r-concavity and related concepts," ECON - Working Papers 187, Department of Economics - University of Zurich.
    11. Rota-Graziosi, Grégoire, 2019. "The supermodularity of the tax competition game," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 25-35.
    12. Corchón, Luis C. & Torregrosa, Ramón J., 2020. "Cournot equilibrium revisited," Mathematical Social Sciences, Elsevier, vol. 106(C), pages 1-10.
    13. von Mouche, Pierre & Szidarovszky, Ferenc, 2024. "Aggregative games with discontinuous payoffs at the origin," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 77-84.

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    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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