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Aggregative games with discontinuous payoffs at the origin

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  • von Mouche, Pierre
  • Szidarovszky, Ferenc

Abstract

Recently a framework was developed for aggregative variational inequalities by means of the Selten–Szidarovszky technique. By referring to this framework, a powerful Nash equilibrium uniqueness theorem for sum-aggregative games is derived. Payoff functions are strictly quasi-concave in own strategies but may be discontinuous at the origin. Its power is illustrated by reproducing and generalising in a few lines an equilibrium uniqueness result in Corchón and Torregrosa (2020) for Cournot oligopolies with the Bulow–Pfleiderer price function. Another illustration addresses an asymmetric contest with endogenous valuations in Hirai and Szidarovszky (2013).

Suggested Citation

  • von Mouche, Pierre & Szidarovszky, Ferenc, 2024. "Aggregative games with discontinuous payoffs at the origin," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 77-84.
    • Handle: RePEc:eee:matsoc:v:129:y:2024:i:c:p:77-84
    DOI: 10.1016/j.mathsocsci.2024.03.008
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    References listed on IDEAS

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    1. Szidarovszky, F & Yakowitz, S, 1977. "A New Proof of the Existence and Uniqueness of the Cournot Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 787-789, October.
    2. Peter Hubert Mathieu Mouche & Ferenc Szidarovszky, 2023. "Aggregative Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1056-1092, March.
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    6. Corchón, Luis C. & Torregrosa, Ramón J., 2020. "Cournot equilibrium revisited," Mathematical Social Sciences, Elsevier, vol. 106(C), pages 1-10.
    7. Tan, Kok-Keong & Yu, Jian & Yuan, Xian-Zhi, 1995. "Existence Theorems of Nash Equilibria for Non-cooperative N-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(3), pages 217-222.
    8. Shumei Hirai & Ferenc Szidarovszky, 2013. "Existence And Uniqueness Of Equilibrium In Asymmetric Contests With Endogenous Prizes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-9.
    9. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
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