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Generalization of Zhou fixed point theorem

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  • Lu Yu

Abstract

We give two generalizations of the Zhou fixed point theorem. They weaken the subcompleteness condition of values, and relax the ascending condition of the correspondence. As an application, we derive a generalization of Topkis's theorem on the existence and order structure of the set of Nash equilibria of supermodular games.

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  • Lu Yu, 2024. "Generalization of Zhou fixed point theorem," Papers 2407.17884, arXiv.org.
    • Handle: RePEc:arx:papers:2407.17884
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    References listed on IDEAS

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    1. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    2. Sabarwal, Tarun, 2025. "General theory of equilibrium in models with complementarities," Journal of Economic Theory, Elsevier, vol. 224(C).
    3. Prokopovych, Pavlo & Yannelis, Nicholas C., 2017. "On strategic complementarities in discontinuous games with totally ordered strategies," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 147-153.
    4. Federico Echenique, 2005. "A short and constructive proof of Tarski’s fixed-point theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 215-218, June.
    5. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.
    6. Lu Yu, 2024. "Nash equilibria of games with generalized complementarities," Papers 2407.00636, arXiv.org.
    7. Lu Yu, 2024. "Existence and structure of Nash equilibria for supermodular games," Papers 2406.09582, arXiv.org.
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    Cited by:

    1. Lu Yu, 2024. "Order-theoretical fixed point theorems for correspondences and application in game theory," Papers 2407.18582, arXiv.org.

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