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Strongly Consistent Self-Confirming Equilibrium

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  • Yuichiro Kamada

Abstract

Fudenberg and Levine (1993a) introduced the notion of self-confirming equilibrium, which is generally less restrictive than Nash equilibrium. Fudenberg and Levine also defined a concept of consistency, and claimed in their Theorem 4 that with consistency and other conditions on beliefs, a self-confirming equilibrium has a Nash equilibrium outcome. We provide a counterexample that disproves Theorem 4 and prove an alternative by replacing consistency with a more restrictive concept, which we call strong consistency. In games with observed deviators, self-confirming equilibria are strongly consistent self-confirming equilibria. Hence, our alternative theorem ensures that despite the counterexample, the corollary of Theorem 4 is still valid. Copyright 2010 The Econometric Society.

Suggested Citation

  • Yuichiro Kamada, 2010. "Strongly Consistent Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 78(2), pages 823-832, March.
    • Handle: RePEc:ecm:emetrp:v:78:y:2010:i:2:p:823-832
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    Cited by:

    1. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. Shimoji, Makoto, 2012. "Outcome-equivalence of self-confirming equilibrium and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 441-447.
    3. , & ,, 2015. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, vol. 10(3), September.
    4. Pierpaolo Battigalli & Alfredo Di Tillio & Dov Samet, 2011. "Strategies and interactive beliefs in dynamic games," Working Papers 375, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    5. Gamba, Astrid & Regner, Tobias, 2019. "Preferences-dependent learning in the centipede game: The persistence of mistrust," European Economic Review, Elsevier, vol. 120(C).

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