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

Author

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  • 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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    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.
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    2. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    3. Takashi Kamihigashi & Kerim Keskin & Çağrı Sağlam, 2021. "Organizational refinements of Nash equilibrium," Theory and Decision, Springer, vol. 91(3), pages 289-312, October.
    4. Balbus, Łukasz & Olszewski, Wojciech & Reffett, Kevin & Woźny, Łukasz, 2025. "A Tarski–Kantorovich theorem for correspondences," Journal of Mathematical Economics, Elsevier, vol. 118(C).
    5. Molinari, Francesca, 2020. "Microeconometrics with partial identification," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 355-486, Elsevier.
    6. 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.
    7. 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.
    8. Emin Karagözoğlu & Kerim Keskin & Çağrı Sağlam, 2024. "Submodularity and supermodularity in contest games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 20(2), pages 182-198, June.
    9. 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.
    10. Lu Yu, 2024. "Generalization of Zhou fixed point theorem," Papers 2407.17884, arXiv.org.
    11. Jain, Ritesh & Lombardi, Michele & Müller, Christoph, 2023. "An alternative equivalent formulation for robust implementation," Games and Economic Behavior, Elsevier, vol. 142(C), pages 368-380.
    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. 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.
    15. 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.
    16. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.
    17. Alex Bloedel & R. Vijay Krishna & Oksana Leukhina, 2025. "Extended Supplement to “Insurance and Inequality with Persistent Private Information”," Working Papers 2025-012, Federal Reserve Bank of St. Louis.
    18. Miyauchi, Yuhei, 2016. "Structural estimation of pairwise stable networks with nonnegative externality," Journal of Econometrics, Elsevier, vol. 195(2), pages 224-235.
    19. Azham Ilyass & Naveen Mani & Rahul Shukla, 2025. "Reich Graph Contraction in Graphically Extended b‐Metric Spaces With Applications to Cantilever Beam Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    20. 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 11 Aug 2024.
    21. Muhammad Shoaib & Muhammad Sarwar & Kamal Shah & Nabil Mlaiki, 2022. "Common Fixed Point Results via Set‐Valued Generalized Weak Contraction with Directed Graph and Its Application," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    22. Jaeok Park & Doo Hyung Yun, 2023. "Possibilistic beliefs in strategic games," Theory and Decision, Springer, vol. 95(2), pages 205-228, August.
    23. 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.
    24. 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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    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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