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A Unifying Approach to Existence of Nash Equilibrium

Author

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  • Balder, Erik J

Abstract

An approach initiated in [4] is shown to unify results about the existence of (1) Nash equilibria in games with at most countably many players, (2) Cournot-Nash equilibrium distributions for large, anonymous games, and (3) Nash equilibria (both mixed and pure) for continuum games. A new, central notion of mixed externality is developed for this purpose.

Suggested Citation

  • Balder, Erik J, 1995. "A Unifying Approach to Existence of Nash Equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 79-94.
    • Handle: RePEc:spr:jogath:v:24:y:1995:i:1:p:79-94
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    Cited by:

    1. Camacho, Carmen & Kamihigashi, Takashi & Sağlam, Çağrı, 2018. "Robust comparative statics for non-monotone shocks in large aggregative games," Journal of Economic Theory, Elsevier, vol. 174(C), pages 288-299.
    2. Yang, Zhe, 2020. "The weak α-core of exchange economies with a continuum of players and pseudo-utilities," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 43-50.
    3. Balder, Erik J., 2000. "Incompatibility of Usual Conditions for Equilibrium Existence in Continuum Economies without Ordered Preferences," Journal of Economic Theory, Elsevier, vol. 93(1), pages 110-117, July.
    4. Wei He & Yeneng Sun, 2018. "Conditional expectation of correspondences and economic applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 265-299, August.
    5. Agnieszka Wiszniewska-Matyszkiel, 2014. "Open and Closed Loop Nash Equilibria in Games with a Continuum of Players," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 280-301, January.
    6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2012. "Social Decision Theory: Choosing within and between Groups," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1591-1636.
    7. Jian Yang, 2021. "Analysis of Markovian Competitive Situations Using Nonatomic Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 184-216, March.
    8. Youcef Askoura, 2019. "On the core of normal form games with a continuum of players : a correction," Papers 1903.09819, arXiv.org.
    9. Peter Helgesson & Bernt Wennberg, 2015. "The N-Player War of Attrition in the Limit of Infinitely Many Players," Dynamic Games and Applications, Springer, vol. 5(1), pages 65-93, March.
    10. Balder, Erik J., 2008. "More on equilibria in competitive markets with externalities and a continuum of agents," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 575-602, July.
    11. Sun, Xiang & Zeng, Yishu, 2020. "Perfect and proper equilibria in large games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 288-308.
    12. Balder, Erik J., 2003. "On undominated Nash equilibria for games with a measure space of players," Economics Letters, Elsevier, vol. 80(2), pages 137-140, August.
    13. Agnieszka Wiszniewska-Matyszkiel, 2016. "Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information," Annals of Operations Research, Springer, vol. 243(1), pages 147-177, August.
    14. Askoura, Y., 2017. "On the core of normal form games with a continuum of players," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 32-42.
    15. Agnieszka Wiszniewska-Matyszkiel, 2017. "Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 984-1007, March.
    16. Xinmin Hu & Daniel Ralph, 2007. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Operations Research, INFORMS, vol. 55(5), pages 809-827, October.
    17. Fabio Maccheroni Jr. & Massimo Marinacci Jr. & Aldo Rustichini Jr., 2014. "Pride and Diversity in Social Economies," American Economic Journal: Microeconomics, American Economic Association, vol. 6(4), pages 237-271, November.
    18. Wiszniewska-Matyszkiel, Agnieszka, 2005. "Stock market as a dynamic game with continuum of players," MPRA Paper 32982, University Library of Munich, Germany, revised 2006.
    19. Filipe Martins-da-Rocha, V. & Topuzu, Mihaela, 2008. "Cournot-Nash equilibria in continuum games with non-ordered preferences," Journal of Economic Theory, Elsevier, vol. 140(1), pages 314-327, May.
    20. Yang, Jian, 2022. "A Bayesian nonatomic game and its applicability to finite-player situations," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    21. Hu, X. & Ralph, R., 2006. "Using EPECs to model bilevel games in restructured electricity markets with locational prices," Cambridge Working Papers in Economics 0619, Faculty of Economics, University of Cambridge.
    22. Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, vol. 102(2), pages 437-470, February.
    23. Jian Yang, 2023. "Nonatomic game with general preferences over returns," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 861-889, September.

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