IDEAS home Printed from https://ideas.repec.org/p/wrk/warwec/952.html
   My bibliography  Save this paper

P-Stable Equilibrium : Definition and Some Properties

Author

Listed:
  • Desgranges, Gabriel

    (Université de Cergy-Pontoise)

  • Ghosal, Sayantan

    (University of Warwick)

Abstract

We define a continuous index of strategic stability,p.stability, which requires equilibrium to be the unique outcome compatible with common knowledge of rationality and common knowledge of p.beliefs (beliefs that put probability at least p on the equilibrium profile). We show that every equilibrium (within a large class) is p-stable for some p

Suggested Citation

  • Desgranges, Gabriel & Ghosal, Sayantan, 2010. "P-Stable Equilibrium : Definition and Some Properties," The Warwick Economics Research Paper Series (TWERPS) 952, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:952
    as

    Download full text from publisher

    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2010/twerp_952.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hu, Tai-Wei, 2007. "On p-rationalizability and approximate common certainty of rationality," Journal of Economic Theory, Elsevier, vol. 136(1), pages 379-391, September.
    2. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    3. Codognato, Giulio & Ghosal, Sayantan, 2000. "Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 39-53, August.
    4. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
    5. CODOGNATO, Giulio, 2000. "Cournot-Nash equilibria in limit exchange economies with complete markets: A comparison between two models," LIDAM Reprints CORE 1445, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Codognato, Giulio, 2000. "Cournot-Nash Equilibria in Limit Exchange Economies with Complete Markets: A Comparison between Two Models," Games and Economic Behavior, Elsevier, vol. 31(1), pages 136-146, April.
    7. Sahi, Siddhartha & Yao, Shuntian, 1989. "The non-cooperative equilibria of a trading economy with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 325-346, September.
    8. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
    9. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    10. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Dubey, Pradeep & Shapley, Lloyd S., 1994. "Noncooperative general exchange with a continuum of traders: Two models," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 253-293, May.
    12. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    13. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    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. Desgranges, Gabriel & Gauthier, Stéphane, 2016. "Rationalizability and efficiency in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 163-176.
    2. George W Evans & Roger Guesnerie & Bruce McGough, 2019. "Eductive Stability in Real Business Cycle Models," Economic Journal, Royal Economic Society, vol. 129(618), pages 821-852.

    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. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2012. "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem," The Warwick Economics Research Paper Series (TWERPS) 994, University of Warwick, Department of Economics.
    2. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2011. "Noncooperative oligopoly in markets with a continuum of traders," Games and Economic Behavior, Elsevier, vol. 72(1), pages 38-45, May.
    3. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic Julien & Simone Tonin, 2020. "Existence and optimality of Cournot–Nash equilibria in a bilateral oligopoly with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 933-951, December.
    4. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    5. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 837, University of Warwick, Department of Economics.
    6. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan & Julien, Ludovic & Tonin, Simone, 2018. "Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 478-485.
    7. Ghosal, Sayantan & Tonin, Simone, 2018. "Noncooperative oligopoly in economies with infinitely many commodities and traders," Games and Economic Behavior, Elsevier, vol. 109(C), pages 184-200.
    8. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, 2017. "Asymptotic equivalence between Cournot–Nash and Walras equilibria in exchange economies with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 975-990, November.
    9. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2014. "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem µa la Cournot," SIRE Discussion Papers 2014-019, Scottish Institute for Research in Economics (SIRE).
    11. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2020. "Atomic Leontievian Cournotian traders are always Walrasian," Games and Economic Behavior, Elsevier, vol. 122(C), pages 318-327.
    12. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    13. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, "undated". "Noncooperative oligopoly in markets with a continuum of traders: a limit theorem a la Cournot," Working Papers 2014_01, Business School - Economics, University of Glasgow.
    14. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Economics Letters, Elsevier, vol. 207(C).
    15. Geir B. Asheim & Mark Voorneveld & Jörgen Weibull, 2009. "Epistemically stable strategy sets," Working Papers hal-00440098, HAL.
    16. Ludovic A. Julien & Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Damiano Turchet, 2023. "Noncooperative Oligopoly in Markets with a Continuum of Traders and a Strongly Connected Set of Commodities: A Limit Theorem," EconomiX Working Papers 2023-22, University of Paris Nanterre, EconomiX.
    17. Julien, Ludovic A., 2013. "On Stackelberg competition in strategic multilateral exchange," Research in Economics, Elsevier, vol. 67(1), pages 59-75.
    18. Dubey, Pradeep & Sahi, Siddhartha & Shubik, Martin, 2018. "Money as minimal complexity," Games and Economic Behavior, Elsevier, vol. 108(C), pages 432-451.
    19. Pradeep Dubey & Siddhartha Sahi & Martin Shubik, 2014. "Minimally complex exchange mechanisms: Emergence of prices, markets, and money," Department of Economics Working Papers 14-01, Stony Brook University, Department of Economics.
    20. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.

    More about this item

    Keywords

    common knowledge ; strategic uncertainty ; rationalizability. JEL Classification: C70 ; D84;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods

    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:wrk:warwec:952. 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: Margaret Nash (email available below). General contact details of provider: https://edirc.repec.org/data/dewaruk.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.