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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, University Library of Munich, Germany.
    • 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. R Jain & V Korpela & M Lombardi, 2021. "An Iterative Approach to Rationalizable Implementation," IEAS Working Paper : academic research 21-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    2. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    3. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.
    4. Takashi Kamihigashi & Kerim Keskin & Çağrı Sağlam, 2021. "Organizational refinements of Nash equilibrium," Theory and Decision, Springer, vol. 91(3), pages 289-312, October.
    5. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    6. Matthew Elliott & Benjamin Golub & Matthew V. Leduc, 2022. "Supply Network Formation and Fragility," American Economic Review, American Economic Association, vol. 112(8), pages 2701-2747, August.
    7. Miyauchi, Yuhei, 2016. "Structural estimation of pairwise stable networks with nonnegative externality," Journal of Econometrics, Elsevier, vol. 195(2), pages 224-235.
    8. Özlem Acar & Hassen Aydi & Manuel De la Sen, 2021. "New Fixed Point Results via a Graph Structure," Mathematics, MDPI, vol. 9(9), pages 1-13, April.
    9. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    10. Robert A. Becker & Juan Pablo Rincón-Zapatero, 2017. "Arbitration and Renegotiation in Trade Agreements," CAEPR Working Papers 2017-007, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    11. Alex Bloedel & R. Vijay Krishna & Oksana Leukhina, 2018. "Insurance and Inequality with Persistent Private Information," Working Papers 2018-020, Federal Reserve Bank of St. Louis, revised 12 Dec 2021.
    12. Robert Becker & Juan Pablo Rincon-Zapatero, 2018. "Recursive Utility and Thompson Aggregators, I: Constructive Existence Theory for the Koopmans Equation," CAEPR Working Papers 2018-006, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    13. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Jaeok Park & Doo Hyung Yun, 2023. "Possibilistic beliefs in strategic games," Theory and Decision, Springer, vol. 95(2), pages 205-228, August.
    15. 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.
    16. Karagözoğlu, Emin & Keskin, Kerim & Sağlam, Çağrı, 2013. "A minimally altruistic refinement of Nash equilibrium," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 422-430.

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    More about this item

    Keywords

    tarski; fixed-point theorem; supermodular; supermodular games; strategic complementarities; equilibrium existence;
    All these keywords.

    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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