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Equilibrium in discontinuous games without complete or transitive preferences

Author

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  • Philip J. Reny

    (University of Chicago)

Abstract

Reny (Econ Theory, 2015) is used here to prove the existence of equilibrium in discontinuous games in which the players’ preferences need be neither complete nor transitive. The proof adapts important ideas from Shafer and Sonnenschein (J Math Econ 2:345–348, 1975).

Suggested Citation

  • Philip J. Reny, 2016. "Equilibrium in discontinuous games without complete or transitive preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 1-4, April.
    • Handle: RePEc:spr:etbull:v:4:y:2016:i:1:d:10.1007_s40505-015-0087-3
    DOI: 10.1007/s40505-015-0087-3
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    Citations

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    Cited by:

    1. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    2. Konrad Podczeck & Nicholas C. Yannelis, 2022. "Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent and price-dependent preferences, without free disposal, and without compact consumption sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 413-420, April.
    3. Oriol Carbonell-Nicolau & Richard P. McLean, 2019. "Nash and Bayes–Nash equilibria in strategic-form games with intransitivities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 935-965, November.
    4. Bernard Cornet, 2020. "The Gale–Nikaido–Debreu lemma with discontinuous excess demand," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 169-180, October.
    5. Khan, M. Ali & McLean, Richard P. & Uyanik, Metin, 2024. "On constrained generalized games with action sets in non-locally-convex and non-Hausdorff topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    6. Anderson, Robert M. & Duanmu, Haosui & Khan, M. Ali & Uyanik, Metin, 2022. "On abstract economies with an arbitrary set of players and action sets in locally-convex topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    7. Motoki Otsuka, 2024. "The existence of Walrasian equilibrium: infinitely many commodities, measure space of agents, and discontinuous preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 119-140, December.

    More about this item

    Keywords

    Abstract games; Discontinuous games; Incomplete preferences; Nontransitive preferences;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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