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Metastable Equilibria

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  • Srihari Govindan
  • Robert Wilson

Abstract

Metastability is a refinement of the Nash equilibria of a game derived from two conditions: embedding combines behavioral axioms called invariance and small-worlds , and continuity requires games with nearby best replies to have nearby equilibria. These conditions imply that a connected set of Nash equilibria is metastable if it is arbitrarily close to an equilibrium of every sufficiently small perturbation of the best-reply correspondence of every game in which the given game is embedded as an independent subgame. Metastability satisfies the same decision-theoretic properties as Mertens' stronger refinement called stability. Metastability is characterized by a strong form of homotopic essentiality of the projection map from a neighborhood in the graph of equilibria over the space of strategy perturbations. Mertens' definition differs by imposing homological essentiality, which implies a version of small-worlds satisfying a stronger decomposition property. Mertens' stability and metastability select the same outcomes of generic extensive-form games.
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  • Srihari Govindan & Robert Wilson, 2006. "Metastable Equilibria," Levine's Bibliography 122247000000001211, UCLA Department of Economics.
  • Handle: RePEc:cla:levrem:122247000000001211
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Srihari Govindan & Jean-François Mertens, 2004. "An equivalent definition of stable Equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 339-357, June.
    3. Hillas, John & Kohlberg, Elon, 2002. "Foundations of strategic equilibrium," 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 42, pages 1597-1663 Elsevier.
    4. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-1390, November.
    5. Wilson, Robert B. & Govindan, Srihari, 2006. "Sufficient conditions for stable equilibria," Theoretical Economics, Econometric Society, vol. 1(2), pages 167-206, June.
    6. Mclennan, A., 1989. "Selected Topics In The Theory Of Fixed Points," Papers 251, Minnesota - Center for Economic Research.
    7. Jean-François Mertens, 1989. "Stable Equilibria---A Reformulation," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 575-625, November.
    8. Mertens, Jean-Francois, 1992. "The small worlds axiom for stable equilibria," Games and Economic Behavior, Elsevier, vol. 4(4), pages 553-564, October.
    9. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
    10. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    11. Srihari Govindan & Robert Wilson, 2006. "Essential Equilibria," Levine's Bibliography 122247000000001035, UCLA Department of Economics.
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    Cited by:

    1. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
    2. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
    3. Srihari Govindan & Robert Wilson, 2008. "Axiomatic Theory of Equilibrium Selection in Signalling Games with Generic Payoffs," Levine's Working Paper Archive 122247000000002381, David K. Levine.

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