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A note on a Tarski type fixed-point theorem

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  • Roberto Ghiselli Ricci

    (University of Ferrara)

Abstract

In this paper we propose a basic fixed-point theorem for correspondences inspired by Tarski’s intersection point theorem. This result furnishes an efficient tool to prove the existence of pure strategy Nash equilibria for two player games with possibly discontinuous payoffs functions defined on compact real intervals.

Suggested Citation

  • Roberto Ghiselli Ricci, 2021. "A note on a Tarski type fixed-point theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 751-758, September.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:3:d:10.1007_s00182-021-00763-3
    DOI: 10.1007/s00182-021-00763-3
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    References listed on IDEAS

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    1. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    2. Tian, Guoqiang, 2015. "On the existence of equilibria in games with arbitrary strategy spaces and preferences," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 9-16.
    3. Rabia Nessah & Guoqiang Tian, 2008. "The Existence of Equilibria in Discontinuous and Nonconvex Games," Working Papers 2008-ECO-14, IESEG School of Management, revised Mar 2010.
    4. Amir, Rabah & De Castro, Luciano, 2017. "Nash equilibrium in games with quasi-monotonic best-responses," Journal of Economic Theory, Elsevier, vol. 172(C), pages 220-246.
    5. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
    6. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    7. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
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    Cited by:

    1. Aniruddha Ghosh & Mohammed Ali Khan & Metin Uyanik, 2022. "The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation," Games, MDPI, vol. 13(4), pages 1-24, July.

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