IDEAS home Printed from https://ideas.repec.org/p/huj/dispap/dp607.html

A Cantor Set of Games with No Shift-Homogeneous Equilibrium Selection

Author

Listed:
  • Yehuda (John) Levy

Abstract

We construct a continuum of games on a countable set of players that does not possess a measurable equilibrium selection that satisfies a natural homogeneity property. The explicit nature of the construction yields counterexamples to the existence of equilibria in models with overlapping generations and in games with a continuum of players.

Suggested Citation

  • Yehuda (John) Levy, 2012. "A Cantor Set of Games with No Shift-Homogeneous Equilibrium Selection," Discussion Paper Series dp607, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp607
    as

    Download full text from publisher

    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp607.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Galor, Oded, 1992. "A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System," Econometrica, Econometric Society, vol. 60(6), pages 1351-1386, November.
    3. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    4. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808, Elsevier.
    5. Hannu Salonen, 2010. "On the existence of Nash equilibria in large games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 351-357, July.
    6. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Yehuda John Levy, 2016. "Projections and functions of Nash equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 435-459, March.
    2. János Flesch & Arkadi Predtetchinski, 2020. "Parameterized games of perfect information," Annals of Operations Research, Springer, vol. 287(2), pages 683-699, April.
    3. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Equilibria: The Case of Absolutely Continuous Transitions," Discussion Paper Series dp612, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

    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. Yehuda Levy, 2013. "A Cantor Set of Games with No Shift-Homogeneous Equilibrium Selection," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 492-503, August.
    2. Robert M. Anderson & Haosui Duanmu & M. Ali Khan & Metin Uyanik, 2022. "Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 387-412, April.
    3. Teng, Jimmy, 2010. "Bayesian Theory of Games: A Statistical Decision Theoretic Based Analysis of Strategic Interactions," MPRA Paper 24189, University Library of Munich, Germany.
    4. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Schmeidler, David, 2022. "Equilibria of nonatomic anonymous games," Games and Economic Behavior, Elsevier, vol. 135(C), pages 110-131.
    5. Werner Güth, 1991. "Game Theory's Basic Question: Who Is a Player?," Journal of Theoretical Politics, , vol. 3(4), pages 403-435, October.
    6. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.
    7. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225, Elsevier.
    8. Bin Xie & David M. Dilts & Mikhael Shor, 2006. "The physician–patient relationship: the impact of patient‐obtained medical information," Health Economics, John Wiley & Sons, Ltd., vol. 15(8), pages 813-833, August.
    9. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    10. Youcef Askoura, 2019. "On the core of normal form games with a continuum of players : a correction," Papers 1903.09819, arXiv.org.
    11. Wei He & Yeneng Sun, 2018. "Conditional expectation of correspondences and economic applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 265-299, August.
    12. Jibang Wu & Haifeng Xu & Yifan Guo & Weijie Su, 2023. "An Isotonic Mechanism for Overlapping Ownership," Papers 2306.11154, arXiv.org, revised Jun 2025.
    13. van Damme, E.E.C., 2015. "Game theory : Noncooperative games," Other publications TiSEM ff518f2b-501f-4d99-817b-c, Tilburg University, School of Economics and Management.
    14. Guilherme Carmona, 2006. "On a theorem by Mas-Colell," Nova SBE Working Paper Series wp485, Universidade Nova de Lisboa, Nova School of Business and Economics.
    15. Fritz W. Scharpf, 1990. "Games Real Actors Could Play," Rationality and Society, , vol. 2(4), pages 471-494, October.
    16. Jian Yang, 2017. "A link between sequential semi-anonymous nonatomic games and their large finite counterparts," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 383-433, May.
    17. Li, Bingbing & Long, Yan, 2024. "Output Uncertainty Mitigation in Competitive Markets," Center for Mathematical Economics Working Papers 698, Center for Mathematical Economics, Bielefeld University.
    18. Steven J. Bosworth, 2017. "The importance of higher-order beliefs to successful coordination," Experimental Economics, Springer;Economic Science Association, vol. 20(1), pages 237-258, March.
    19. Kalai, Ehud & Shmaya, Eran, 2018. "Large strategic dynamic interactions," Journal of Economic Theory, Elsevier, vol. 178(C), pages 59-81.
    20. Camacho, Carmen & Kamihigashi, Takashi & Sağlam, Çağrı, 2018. "Robust comparative statics for non-monotone shocks in large aggregative games," Journal of Economic Theory, Elsevier, vol. 174(C), pages 288-299.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:huj:dispap:dp607. 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: Michael Simkin (email available below). General contact details of provider: https://edirc.repec.org/data/crihuil.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.