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A Short And Constructive Proof of Tarski's Fixed-Point Theorem

Author

Listed:
  • Federico Echenique

    (California Institute of Technology)

Abstract

I give short and constructive proofs of Tarski's fixed-point theorem, and of a much-used extension of Tarski's fixed-point theorem to set- valued maps.

Suggested Citation

  • Federico Echenique, 2003. "A Short And Constructive Proof of Tarski's Fixed-Point Theorem," GE, Growth, Math methods 0305001, EconWPA.
  • Handle: RePEc:wpa:wuwpge:0305001
    Note: Type of Document - Tex; prepared on Dell PC - Linux; to print on PostScript; pages: 4; figures: non
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0305/0305001.pdf
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    References listed on IDEAS

    as
    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.
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    Cited by:

    1. Robert A. Becker & Juan Pablo Rincón-Zapatero, 2017. "Arbitration and Renegotiation in Trade Agreements," Caepr Working Papers 2017-007 Classification-D, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    2. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.
    3. Takashi Kamihigashi & Kerim Keskin & Çağrı Sağlam, 2017. "Organizational Refinements of Nash Equilibrium," Discussion Paper Series DP2017-25, Research Institute for Economics & Business Administration, Kobe University.
    4. Federico Quartieri, 2013. "Coalition-proofness under weak and strong Pareto dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 553-579, February.
    5. Miyauchi, Yuhei, 2016. "Structural estimation of pairwise stable networks with nonnegative externality," Journal of Econometrics, Elsevier, vol. 195(2), pages 224-235.
    6. Karagözoğlu, Emin & Keskin, Kerim & Sağlam, Çağrı, 2013. "A minimally altruistic refinement of Nash equilibrium," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 422-430.

    More about this item

    Keywords

    tarski; fixed-point theorem; supermodular; supermodular games; strategic complementarities; equilibrium existence;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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