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P-Stable Equilibrium: Definition And Some Properties

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  • Desgranges, Gabriel
  • Ghosal, Sayantan

Abstract

We deÖne a continuous index of strategic stability, pstability, which requires equilibrium to be the unique outcome compatible with common knowledge of rationality and common knowledge of pbeliefs (beliefs that put probability at least p on the equilibrium proÖle). We show that every equilibrium (within a large class) is p-stable for some p < 1 and justify, in smooth settings, the intuition that the slope of the best response map is related to the stability of equilibrium. We show that adding incomplete information on fundamentals could decrease the degree of strategic stability. In two applications to large markets we (i) show that a unique equilibrium globally unstable (under t‚tonnement dynamics) has, nevertheless, a measure of strategic stability, (ii) characterize the conditions under which enhanced equilibrium e¢ ciency results in decreased strategic stability.

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  • Desgranges, Gabriel & Ghosal, Sayantan, 2010. "P-Stable Equilibrium: Definition And Some Properties," Economic Research Papers 270772, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:270772
    DOI: 10.22004/ag.econ.270772
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    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. 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..
    4. 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).
    5. 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.
    6. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    7. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    8. 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.
    9. 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.
    10. Carlsson, H. & van Damme, E.E.C., 1990. "Global games and equilibrium selection," Other publications TiSEM 698f4897-46c6-4097-8265-2, Tilburg University, School of Economics and Management.
    11. Carlsson, H. & van Damme, E.E.C., 1993. "Global games and equilibrium selection," Other publications TiSEM 49a54f00-dcec-4fc1-9488-4, Tilburg University, School of Economics and Management.
    12. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
    13. 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.
    14. 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).
    15. 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.
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    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.

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    Financial Economics;

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    • C - Mathematical and Quantitative Methods

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