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Algorithms for cautious reasoning in games

Author

Listed:
  • Geir B. Asheim

    () (University of Oslo)

  • Andrés Perea

    () (Maastricht University)

Abstract

We provide comparable algorithms for the Dekel–Fudenberg procedure, iterated admissibility, proper rationalizability and full permissibility by means of the notions of likelihood orderings and preference restrictions. The algorithms model reasoning processes whereby each player’s preferences over his own strategies are completed by eliminating likelihood orderings. We apply the algorithms for comparing iterated admissibility, proper rationalizability and full permissibility, and provide a sufficient condition under which iterated admissibility does not rule out properly rationalizable strategies. We also use the algorithms to examine an economically relevant strategic situation, namely a bilateral commitment bargaining game. Finally, we discuss the relevance of our algorithms for epistemic analysis.

Suggested Citation

  • Geir B. Asheim & Andrés Perea, 2019. "Algorithms for cautious reasoning in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1241-1275, December.
  • Handle: RePEc:spr:jogath:v:48:y:2019:i:4:d:10.1007_s00182-019-00680-6
    DOI: 10.1007/s00182-019-00680-6
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    References listed on IDEAS

    as
    1. Dekel, Eddie & Friedenberg, Amanda & Siniscalchi, Marciano, 2016. "Lexicographic beliefs and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 955-985.
    2. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
    3. Perea, Andrés, 2011. "An algorithm for proper rationalizability," Games and Economic Behavior, Elsevier, vol. 72(2), pages 510-525, June.
    4. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    5. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    6. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    7. Yang, Chih-Chun, 2015. "Weak assumption and iterative admissibility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 87-101.
    8. Asheim, Geir B. & Sovik, Ylva, 2005. "Preference-based belief operators," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 61-82, July.
    9. Crawford, Vincent P, 1982. "A Theory of Disagreement in Bargaining," Econometrica, Econometric Society, vol. 50(3), pages 607-637, May.
    10. 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..
    11. Lee, Byung Soo, 2016. "Admissibility and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 42-72.
    12. Tore Ellingsen & Topi Miettinen, 2008. "Commitment and Conflict in Bilateral Bargaining," American Economic Review, American Economic Association, vol. 98(4), pages 1629-1635, September.
    13. Barelli, Paulo & Galanis, Spyros, 2013. "Admissibility and event-rationality," Games and Economic Behavior, Elsevier, vol. 77(1), pages 21-40.
    14. Cubitt, Robin P. & Sugden, Robert, 2011. "The reasoning-based expected utility procedure," Games and Economic Behavior, Elsevier, vol. 71(2), pages 328-338, March.
    15. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 599-615.
    16. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    17. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
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    More about this item

    Keywords

    Non-cooperative games; Proper rationalizability; Iterated admissibility; Bargaining;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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