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On the existence of monotone selections

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  • Kukushkin, Nikolai S.

Abstract

For a correspondence from a partially ordered set to a lattice, three sets of sufficient conditions for the existence of a monotone selection are obtained. (1) The correspondence is weakly ascending while each value is chain-complete. (2) The correspondence is ascending while the target is a sublattice of the Cartesian product of a finite number of chains. (3) Both source and target are chains while the correspondence is generated by the maximization of a strongly acyclic interval order with the single crossing property. The theorems give new sufficient conditions for the existence of (epsilon) Nash equilibria.

Suggested Citation

  • Kukushkin, Nikolai S., 2009. "On the existence of monotone selections," MPRA Paper 14451, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:14451
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    References listed on IDEAS

    as
    1. William Novshek, 1985. "On the Existence of Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 85-98.
    2. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
    3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    4. Smith, Tony E, 1974. "On the Existence of Most-Preferred Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 184-194, February.
    5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    6. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    7. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    8. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    9. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
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    Cited by:

    1. Nikolai Kukushkin, 2013. "Monotone comparative statics: changes in preferences versus changes in the feasible set," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 1039-1060, April.
    2. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.

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    More about this item

    Keywords

    Monotone selection; (weakly) ascending correspondence; interval order; single crossing; (epsilon) Nash equilibrium;
    All these keywords.

    JEL classification:

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

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