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Existence and structure of Nash equilibria for supermodular games

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  • Lu Yu

Abstract

Two theorems announced by Topkis about the topological description of sublattices are proved. They are applied to extend some classical results concerning the existence and the order structure of Nash equilibria of certain supermodular games, with some problems in Zhou's proof corrected.

Suggested Citation

  • Lu Yu, 2024. "Existence and structure of Nash equilibria for supermodular games," Papers 2406.09582, arXiv.org.
    • Handle: RePEc:arx:papers:2406.09582
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    File URL: http://arxiv.org/pdf/2406.09582
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    References listed on IDEAS

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    1. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Braouezec, Yann & Kiani, Keyvan, 2023. "Economic foundations of generalized games with shared constraint: Do binding agreements lead to less Nash equilibria?," European Journal of Operational Research, Elsevier, vol. 308(1), pages 467-479.
    4. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    5. repec:ebl:ecbull:v:3:y:2002:i:22:p:1-6 is not listed on IDEAS
    6. Friedman, James W. & Mezzetti, Claudio, 2001. "Learning in Games by Random Sampling," Journal of Economic Theory, Elsevier, vol. 98(1), pages 55-84, May.
    7. Tetsuo Yamamori & Satoru Takahashi, 2002. "The pure Nash equilibrium property and the quasi-acyclic condition," Economics Bulletin, AccessEcon, vol. 3(22), pages 1-6.
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    Cited by:

    1. Lu Yu, 2024. "Generalization of Zhou fixed point theorem," Papers 2407.17884, arXiv.org.
    2. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.

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