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On the equivalence between iterated application of choice rules and common belief of applying these rules

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  • Trost, Michael

Abstract

In this paper, we detect meaningful properties of choice rules ensuring that the solution generated by iterated application of choice rules specifies the strategy profiles that might be realized by players who follow these rules and commonly believe this. Our main result is based on four substantial assumptions on choice rules. Whenever the players' choices rules satisfy - besides the technical assumption of regularity - the properties of reflexivity, monotonicity, Aizerman's property, and the independence of payoff equivalent conditions, then such coincidence occurs. This result proves to be strict in the following sense. None of the four substantial properties can be omitted without eliminating the coincidence.

Suggested Citation

  • Trost, Michael, 2019. "On the equivalence between iterated application of choice rules and common belief of applying these rules," Games and Economic Behavior, Elsevier, vol. 116(C), pages 1-37.
    • Handle: RePEc:eee:gamebe:v:116:y:2019:i:c:p:1-37
    DOI: 10.1016/j.geb.2019.03.015
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    1. Galeazzi, Paolo & Marti, Johannes, 2023. "Choice structures in games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 431-455.
    2. Paolo Galeazzi & Johannes Marti, 2023. "Choice Structures in Games," Papers 2304.11575, arXiv.org.

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    More about this item

    Keywords

    Iterative deletion procedure; Common belief; Choice rule; Epistemic game theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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