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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.

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  • 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. Martin Dufwenberg & Mark Stegeman, 2002. "Existence and Uniqueness of Maximal Reductions Under Iterated Strict Dominance," Econometrica, Econometric Society, vol. 70(5), pages 2007-2023, September.
    2. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    3. repec:ebl:ecbull:v:3:y:2005:i:7:p:1-6 is not listed on IDEAS
    4. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    5. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    8. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    9. Alexander Zimper, 2005. "Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-6.
    10. Jürg Niehans, 1948. "Zur Preisbildungen bei ungewissen Erwartungen," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 84(V), pages 433-456.
    11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    12. Mounir, Angie & Perea, Andrés & Tsakas, Elias, 2018. "Common belief in approximate rationality," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 6-16.
    13. Borgers, Tilman, 1993. "Pure Strategy Dominance," Econometrica, Econometric Society, vol. 61(2), pages 423-430, March.
    14. Schwartz, Thomas, 1976. "Choice functions, "rationality" conditions, and variations on the weak axiom of revealed preference," Journal of Economic Theory, Elsevier, vol. 13(3), pages 414-427, December.
    15. Zimper, Alexander, 2005. "Equivalence between best responses and undominated," Papers 05-08, Sonderforschungsbreich 504.
    16. Michael Trost, 2014. "An Epistemic Rationale For Order Independence," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-37.
    17. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 1-12, September.
    18. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    19. Mariotti, Thomas & Meier, Martin & Piccione, Michele, 2005. "Hierarchies of beliefs for compact possibility models," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 303-324, April.
    20. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
    21. Krzysztof R. Apt & Jonathan A. Zvesper, 2010. "The Role of Monotonicity in the Epistemic Analysis of Strategic Games," Games, MDPI, vol. 1(4), pages 1-14, October.
    22. Halpern, Joseph Y. & Pass, Rafael, 2012. "Iterated regret minimization: A new solution concept," Games and Economic Behavior, Elsevier, vol. 74(1), pages 184-207.
    23. Mariotti, Thomas, 2003. "Hierarchies of compact beliefs and rationalizable behavior," Economics Letters, Elsevier, vol. 79(2), pages 199-204, May.
    24. Adam Brandenburger, 2014. "The Language of Game Theory:Putting Epistemics into the Mathematics of Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8844, January.
    25. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    26. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
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    Cited by:

    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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