IDEAS home Printed from https://ideas.repec.org/p/hhs/osloec/2017_010.html
   My bibliography  Save this paper

Algorithms for cautious reasoning in games

Author

Listed:

Abstract

We provide comparable algorithms for the Dekel-Fudenberg procedure, iterated admissibility, proper rationalizability and full permissibility by means of the concepts of preference restrictions and 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. Finally, we use the algorithms to examine an economically relevant strategic situation, namely a bilateral commitment bargaining game.

Suggested Citation

  • Asheim, Geir B. & Perea, Andrés, 2017. "Algorithms for cautious reasoning in games," Memorandum 10/2017, Oslo University, Department of Economics, revised 19 Nov 2018.
    • Handle: RePEc:hhs:osloec:2017_010
    as

    Download full text from publisher

    File URL: http://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2017/memo-10-2017.pdf
    Download Restriction: no
    File URL: https://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2017/memo-10-2017-2.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
    2. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396.
    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. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
    6. Yang, Chih-Chun, 2015. "Weak assumption and iterative admissibility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 87-101.
    7. Asheim, Geir B. & Sovik, Ylva, 2005. "Preference-based belief operators," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 61-82, July.
    8. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    9. 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..
    10. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915.
    11. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 453-478.
    12. Lee, Byung Soo, 2016. "Admissibility and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 42-72.
    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. Geir B. Asheim & Martin Dufwenberg, 2003. "Deductive Reasoning in Extensive Games," Economic Journal, Royal Economic Society, vol. 113(487), pages 305-325, April.
    17. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
    18. Dekel, Eddie & Friedenberg, Amanda & Siniscalchi, Marciano, 2016. "Lexicographic beliefs and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 955-985.
    19. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    20. Crawford, Vincent P, 1982. "A Theory of Disagreement in Bargaining," Econometrica, Econometric Society, vol. 50(3), pages 607-637, May.
    21. Tore Ellingsen & Topi Miettinen, 2008. "Commitment and Conflict in Bilateral Bargaining," American Economic Review, American Economic Association, vol. 98(4), pages 1629-1635, September.
    22. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cubitt, Robin P. & Sugden, Robert, 2011. "The reasoning-based expected utility procedure," Games and Economic Behavior, Elsevier, vol. 71(2), pages 328-338, March.
    2. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    3. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    4. Cubitt, Robin P. & Sugden, Robert, 2011. "The reasoning-based expected utility procedure," Games and Economic Behavior, Elsevier, vol. 71(2), pages 328-338, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2019. "Comprehensive rationalizability," Games and Economic Behavior, Elsevier, vol. 116(C), pages 185-202.
    3. Burkhard Schipper & Martin Meier & Aviad Heifetz, 2017. "Comprehensive Rationalizability," Working Papers 174, University of California, Davis, Department of Economics.
    4. Catonini, Emiliano & De Vito, Nicodemo, 2020. "Weak belief and permissibility," Games and Economic Behavior, Elsevier, vol. 120(C), pages 154-179.
    5. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    6. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    7. Shuige Liu, 2021. "Characterizing permissibility, proper rationalizability, and iterated admissibility by incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 119-148, March.
    8. Adam Brandenburger & Amanda Friedenberg, 2014. "Self-Admissible Sets," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 8, pages 213-249, World Scientific Publishing Co. Pte. Ltd..
    9. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    10. Barelli, Paulo & Galanis, Spyros, 2013. "Admissibility and event-rationality," Games and Economic Behavior, Elsevier, vol. 77(1), pages 21-40.
    11. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    12. Shuige Liu, 2018. "Characterizing Permissibility, Proper Rationalizability, and Iterated Admissibility by Incomplete Information," Papers 1811.01933, arXiv.org.
    13. Shuige Liu, 2018. "Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model," Papers 1801.08767, arXiv.org.
    14. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    15. V. K. Oikonomou & J. Jost, 2020. "Periodic Strategies II: Generalizations and Extensions," Papers 2005.12832, arXiv.org.
    16. Shuige Liu, 2018. "Characterizing Assumption of Rationality by Incomplete Information," Papers 1801.04714, arXiv.org.
    17. Dekel, Eddie & Friedenberg, Amanda & Siniscalchi, Marciano, 2016. "Lexicographic beliefs and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 955-985.
    18. Perea, Andrés, 2011. "An algorithm for proper rationalizability," Games and Economic Behavior, Elsevier, vol. 72(2), pages 510-525, June.
    19. Balkenborg, Dieter, 2018. "Rationalizability and logical inference," Games and Economic Behavior, Elsevier, vol. 110(C), pages 248-257.
    20. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.

    More about this item

    Keywords

    Non-cooperative games; proper rationalizability; iterated admissibility; bargaining;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:osloec:2017_010. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mari Strønstad Øverås (email available below). General contact details of provider: https://edirc.repec.org/data/souiono.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.