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Metastable Equilibria

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  • Srihari Govindan

    (Economics Department, University of Iowa, Iowa City, Iowa 52242)

  • Robert Wilson

    (Stanford Business School, Stanford, California 94305)

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.

Suggested Citation

  • Srihari Govindan & Robert Wilson, 2008. "Metastable Equilibria," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 787-820, November.
  • Handle: RePEc:inm:ormoor:v:33:y:2008:i:4:p:787-820
    DOI: 10.1287/moor.1080.0336
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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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