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Belief in the opponentsʼ future rationality

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  • Perea, Andrés

Abstract

For dynamic games we consider the idea that a player, at every stage of the game, will always believe that his opponents will choose rationally in the future. This is the basis for the concept of common belief in future rationality, which we formalize within an epistemic model. We present an iterative procedure, backward dominance, that proceeds by eliminating strategies from the game, based on strict dominance arguments. We show that the backward dominance procedure selects precisely those strategies that can rationally be chosen under common belief in future rationality if we would not impose (common belief in) Bayesian updating.

Suggested Citation

  • Perea, Andrés, 2014. "Belief in the opponentsʼ future rationality," Games and Economic Behavior, Elsevier, vol. 83(C), pages 231-254.
  • Handle: RePEc:eee:gamebe:v:83:y:2014:i:c:p:231-254
    DOI: 10.1016/j.geb.2013.11.008
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Zuazo-Garin, Peio, 2017. "Uncertain information structures and backward induction," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 135-151.
    2. Rich, Patricia, 2015. "Rethinking common belief, revision, and backward induction," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 102-114.
    3. repec:eee:jetheo:v:169:y:2017:i:c:p:489-516 is not listed on IDEAS
    4. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    5. Bonanno, Giacomo, 2014. "A doxastic behavioral characterization of generalized backward induction," Games and Economic Behavior, Elsevier, vol. 88(C), pages 221-241.
    6. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    7. Aviad Heifetz & Andrés Perea, 2015. "On the outcome equivalence of backward induction and extensive form rationalizability," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 37-59, February.
    8. Miettinen, Topi & Perea, Andrés, 2015. "Commitment in alternating offers bargaining," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 12-18.
    9. Xu, Zibo, 2016. "Convergence of best-response dynamics in extensive-form games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 21-54.

    More about this item

    Keywords

    Epistemic game theory; Dynamic games; Belief in future rationality; Backwards rationalizability procedure; Backward dominance procedure; Backward induction;

    JEL classification:

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

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