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A short and constructive proof of Tarski’s fixed-point theorem

Author

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  • Federico Echenique

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.
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Suggested Citation

  • Federico Echenique, 2005. "A short and constructive proof of Tarski’s fixed-point theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 215-218, June.
    • Handle: RePEc:spr:jogath:v:33:y:2005:i:2:p:215-218
    DOI: 10.1007/s001820400192
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    Citations

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    Cited by:

    1. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    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, 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. 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.
    6. Miyauchi, Yuhei, 2016. "Structural estimation of pairwise stable networks with nonnegative externality," Journal of Econometrics, Elsevier, vol. 195(2), pages 224-235.
    7. 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.
    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. 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.
    10. 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.
    11. 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.
    12. Lu Yu, 2024. "Generalization of Zhou fixed point theorem," Papers 2407.17884, arXiv.org.
    13. 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.
    14. 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.
    15. 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.
    16. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. 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.
    18. Jaeok Park & Doo Hyung Yun, 2023. "Possibilistic beliefs in strategic games," Theory and Decision, Springer, vol. 95(2), pages 205-228, August.
    19. 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.
    20. Karagözoğlu, Emin & Keskin, Kerim & Sağlam, Çağrı, 2013. "A minimally altruistic refinement of Nash equilibrium," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 422-430.
    21. 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.

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    Keywords

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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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