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Order-theoretical fixed point theorems for correspondences and application in game theory

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  • Lu Yu

Abstract

For an ascending correspondence $F:X\to 2^X$ with chain-complete values on a complete lattice $X$, we prove that the set of fixed points is a complete lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets that are not necessarily lattices, we generalize the Abian-Brown and the Markowsky fixed point theorems from single-valued maps to multivalued correspondences. We provide an application in game theory.

Suggested Citation

  • Lu Yu, 2024. "Order-theoretical fixed point theorems for correspondences and application in game theory," Papers 2407.18582, arXiv.org.
    • Handle: RePEc:arx:papers:2407.18582
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    References listed on IDEAS

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    1. Sabarwal, Tarun, 2025. "General theory of equilibrium in models with complementarities," Journal of Economic Theory, Elsevier, vol. 224(C).
    2. Lu Yu, 2024. "Generalization of Zhou fixed point theorem," Papers 2407.17884, arXiv.org.
    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. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.
    5. Lu Yu, 2024. "Nash equilibria of games with generalized complementarities," Papers 2407.00636, arXiv.org.
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    Cited by:

    1. Tarun Sabarwal, 2021. "Order Nearest Comparative Statics of Equilibria," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202517, University of Kansas, Department of Economics, revised Dec 2025.

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