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Common belief in future and restricted past rationality

Author

Listed:
  • Rubén Becerril-Borja

    (Universidad Autónoma Metropolitana-Iztapalapa
    Maastricht University)

  • Andrés Perea

    (Maastricht University)

Abstract

We introduce the idea that a player believes at every stage of a dynamic game that his opponents will choose rationally in the future and have chosen rationally in a restricted way in the past. This is summarized by the concept of common belief in future and restricted past rationality, which is defined epistemically. Moreover, it is shown that every properly rationalizable strategy of the normal form of a dynamic game can be chosen in the dynamic game under common belief in future and restricted past rationality. We also present an algorithm that uses strict dominance, and show that it selects exactly those strategies that can be chosen under common belief in future and restricted past rationality.

Suggested Citation

  • Rubén Becerril-Borja & Andrés Perea, 2020. "Common belief in future and restricted past rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 711-747, September.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:3:d:10.1007_s00182-020-00716-2
    DOI: 10.1007/s00182-020-00716-2
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    References listed on IDEAS

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    More about this item

    Keywords

    Epistemic game theory; Dynamic games; Proper rationalizability; Belief in future rationality; Belief in restricted past rationality;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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