IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/41300.html
   My bibliography  Save this paper

The Maximum Theorem and the Existence of Nash Equilibrium of (Generalized) Games without Lower Semicontinuities

Author

Listed:
  • Tian, Guoqiang
  • Zhou, Jianxin

Abstract

In this paper we generalize Berge's Maximum Theorem to the case where the payoff (utility) functions and the feasible action correspondences are not lowersemicontinuous. The condition we introduced is called the Feasible Path Transfer Lower Semicontinuity (in short, FPT l.s.c.). By applying our Maximum Theorem to game theory and economics, we are able to prove the existence of equilibrium for the generalized games (the so-called abstract economics) and Nash equilibrium for games where the payoff functions and the feasible strategy correspondences are not lowersemicontinuous. Thus the existence theorems given in this paper generalize many existence theorems on Nash equilibrium and equilibrium for the generalized games in the literature.

Suggested Citation

  • Tian, Guoqiang & Zhou, Jianxin, 1990. "The Maximum Theorem and the Existence of Nash Equilibrium of (Generalized) Games without Lower Semicontinuities," MPRA Paper 41300, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41300
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/41300/1/MPRA_paper_41300.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Khan, M. Ali & Vohra, Rajiv, 1984. "Equilibrium in abstract economies without ordered preferences and with a measure space of agents," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 133-142, October.
    2. 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.
    3. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    Full references (including those not matched with items on IDEAS)

    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. Peralta, Susana & Wauthy, Xavier & van Ypersele, Tanguy, 2006. "Should countries control international profit shifting?," Journal of International Economics, Elsevier, vol. 68(1), pages 24-37, January.
    2. Bonatti, Alessandro & Hörner, Johannes, 2017. "Learning to disagree in a game of experimentation," Journal of Economic Theory, Elsevier, vol. 169(C), pages 234-269.
    3. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2018. "Sufficient conditions for weak reciprocal upper semi-continuity in mixed extensions of games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 99-107.
    4. Becchetti, Leonardo & Palestini, Arsen & Solferino, Nazaria & Elisabetta Tessitore, M., 2014. "The socially responsible choice in a duopolistic market: A dynamic model of “ethical product” differentiation," Economic Modelling, Elsevier, vol. 43(C), pages 114-123.
    5. Jacobs, Martin & Requate, Till, 2016. "Bertrand-Edgeworth markets with increasing marginal costs and voluntary trading: Experimental evidence," Economics Working Papers 2016-01, Christian-Albrechts-University of Kiel, Department of Economics.
    6. Bernhardt, Dan & Koufopoulos, Kostas & Trigilia, Giulio, 2022. "Separating equilibria, underpricing and security design," Journal of Financial Economics, Elsevier, vol. 145(3), pages 788-801.
    7. Azevedo, Eduardo M. & Gottlieb, Daniel, 2019. "An example of non-existence of Riley equilibrium in markets with adverse selection," Games and Economic Behavior, Elsevier, vol. 116(C), pages 152-157.
    8. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2020. "A general model of price competition with soft capacity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 95-120, July.
    9. Benjamin Lester & Ali Shourideh & Venky Venkateswaran & Ariel Zetlin-Jones, 2019. "Screening and Adverse Selection in Frictional Markets," Journal of Political Economy, University of Chicago Press, vol. 127(1), pages 338-377.
    10. Xin Zhao, 2018. "Heterogeneity and Unanimity: Optimal Committees with Information Acquisition," Working Paper Series 52, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    11. Mark Armstrong & John Vickers, 2018. "Patterns of Competition with Captive Customers," Economics Series Working Papers 864, University of Oxford, Department of Economics.
    12. Luke Garrod & Matthew Olczak, 2017. "Collusion Under Imperfect Monitoring with Asymmetric Firms," Journal of Industrial Economics, Wiley Blackwell, vol. 65(3), pages 654-682, September.
    13. Plan, Asaf, 2023. "Symmetry in n-player games," Journal of Economic Theory, Elsevier, vol. 207(C).
    14. Amit Pazgal & David Soberman & Raphael Thomadsen, 2016. "Maximal or Minimal Differentiation in a Hotelling Market? A Fresh Perspective," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 3(1), pages 42-47, March.
    15. 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.
    16. Attila Tasnádi, 2016. "Endogenous timing of moves in Bertrand–Edgeworth triopolies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 317-334, December.
    17. Vettas, Nikolaos & Biglaiser, Gary, 2004. "Dynamic Price Competition with Capacity Constraints and Strategic Buyers," CEPR Discussion Papers 4315, C.E.P.R. Discussion Papers.
    18. Hefti, Andreas, 2016. "On the relationship between uniqueness and stability in sum-aggregative, symmetric and general differentiable games," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 83-96.
    19. Heijnen, Pim & Soetevent, Adriaan R., 2018. "Price competition on graphs," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 161-179.
    20. 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.

    More about this item

    Keywords

    Maximum Theorem; Existence; Nash Equilibrium; Lower Semicontinuities;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

    Statistics

    Access and download statistics

    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:pra:mprapa:41300. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.