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Outcome-equivalence of self-confirming equilibrium and Nash equilibrium

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  • Shimoji, Makoto

Abstract

We introduce a condition, Nash-equivalent self-confirming equilibrium. If beliefs are assumed to be independent and unitary, Nash-equivalent self-confirming equilibrium and Nash equilibrium are outcome-equivalent. We show that the set of Nash-equivalent self-confirming equilibria and the set of self-confirming equilibria which are outcome-equivalent to Nash equilibria coincide. Our condition identifies the collection of information sets and requires the existence of beliefs shared by (certain sets of) players regarding these information sets. If the information sets are off the equilibrium path, the beliefs regarding them do not have to be correct. Our condition is weaker than that of strongly consistent self-confirming equilibrium by Kamada (2010).

Suggested Citation

  • Shimoji, Makoto, 2012. "Outcome-equivalence of self-confirming equilibrium and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 441-447.
    • Handle: RePEc:eee:gamebe:v:75:y:2012:i:1:p:441-447
    DOI: 10.1016/j.geb.2011.09.010
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    References listed on IDEAS

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    1. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
    2. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    3. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    4. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    5. Yuichiro Kamada, 2010. "Strongly Consistent Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 78(2), pages 823-832, March.
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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).

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    More about this item

    Keywords

    Nash equilibrium; Self-confirming equilibrium; Extensive-form games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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