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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.

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  • 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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    File URL: http://arxiv.org/pdf/2407.18582
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    References listed on IDEAS

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    1. Lu Yu, 2024. "Generalization of Zhou fixed point theorem," Papers 2407.17884, arXiv.org.
    2. Lu Yu, 2024. "Nash equilibria of games with generalized complementarities," Papers 2407.00636, arXiv.org.
    3. Tarun Sabarwal, 2023. "General theory of equilibrium in models with complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202307, University of Kansas, Department of Economics, revised Sep 2023.
    4. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.
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    1. Lu Yu, 2024. "Generalization of Zhou fixed point theorem," Papers 2407.17884, arXiv.org.
    2. Lu Yu, 2024. "Nash equilibria of games with generalized complementarities," Papers 2407.00636, arXiv.org.

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