IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v50y2021i3d10.1007_s00182-021-00763-3.html
   My bibliography  Save this article

A note on a Tarski type fixed-point theorem

Author

Listed:
  • Roberto Ghiselli Ricci

    (University of Ferrara)

Abstract

In this paper we propose a basic fixed-point theorem for correspondences inspired by Tarski’s intersection point theorem. This result furnishes an efficient tool to prove the existence of pure strategy Nash equilibria for two player games with possibly discontinuous payoffs functions defined on compact real intervals.

Suggested Citation

  • Roberto Ghiselli Ricci, 2021. "A note on a Tarski type fixed-point theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 751-758, September.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:3:d:10.1007_s00182-021-00763-3
    DOI: 10.1007/s00182-021-00763-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-021-00763-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00182-021-00763-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    2. Tian, Guoqiang, 2015. "On the existence of equilibria in games with arbitrary strategy spaces and preferences," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 9-16.
    3. Rabia Nessah & Guoqiang Tian, 2008. "The Existence of Equilibria in Discontinuous and Nonconvex Games," Working Papers 2008-ECO-14, IESEG School of Management, revised Mar 2010.
    4. Amir, Rabah & De Castro, Luciano, 2017. "Nash equilibrium in games with quasi-monotonic best-responses," Journal of Economic Theory, Elsevier, vol. 172(C), pages 220-246.
    5. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aniruddha Ghosh & Mohammed Ali Khan & Metin Uyanik, 2022. "The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation," Games, MDPI, vol. 13(4), pages 1-24, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Plan, Asaf, 2023. "Symmetry in n-player games," Journal of Economic Theory, Elsevier, vol. 207(C).
    2. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.
    3. Tian, Guoqiang, 2015. "On the existence of equilibria in games with arbitrary strategy spaces and preferences," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 9-16.
    4. Tesoriere, Antonio, 2017. "Stackelberg equilibrium with multiple firms and setup costs," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 86-102.
    5. Rabia Nessah, 2022. "Weakly continuous security and nash equilibrium," Theory and Decision, Springer, vol. 93(4), pages 725-745, November.
    6. Rabia Nessah & Guoqiang Tian, 2013. "Existence of Solution of Minimax Inequalities, Equilibria in Games and Fixed Points Without Convexity and Compactness Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 75-95, April.
    7. Rabia Nessah & Guoqiang Tian, 2008. "The Existence of Equilibria in Discontinuous and Nonconvex Games," Working Papers 2008-ECO-14, IESEG School of Management, revised Mar 2010.
    8. Philip J. Reny, 2016. "Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 553-569, March.
    9. Guillaume Roger, 2017. "Two-sided competition with vertical differentiation," Journal of Economics, Springer, vol. 120(3), pages 193-217, April.
    10. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    11. Scalzo, Vincenzo, 2010. "Pareto efficient Nash equilibria in discontinuous games," Economics Letters, Elsevier, vol. 107(3), pages 364-365, June.
    12. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    13. Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.
    14. Albano, Gian Luigi & Matros, Alexander, 2005. "(All) Equilibria in a class of bidding games," Economics Letters, Elsevier, vol. 87(1), pages 61-66, April.
    15. Nessah, Rabia & Tian, Guoqiang, 2008. "Existence of Equilibria in Discontinuous Games," MPRA Paper 41206, University Library of Munich, Germany, revised Mar 2010.
    16. Guoqiang Tian, 2016. "On the existence of price equilibrium in economies with excess demand functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 5-16, April.
    17. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.
    18. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    19. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    20. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Documents de travail du Centre d'Economie de la Sorbonne 12040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:50:y:2021:i:3:d:10.1007_s00182-021-00763-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.