IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v197y2021ics0022053121001435.html
   My bibliography  Save this article

Mixed strategies and preference for randomization in games with ambiguity averse agents

Author

Listed:
  • Calford, Evan M.

Abstract

We study the use of mixed strategies in games by ambiguity averse agents with a preference for randomization. Applying the decision theoretic model of Saito (2015) to games, we establish that the set of rationalizable strategies grows larger as preference for randomization weakens. An agent's preference for randomization is partially observable: given the behavior of an agent in a game, we can determine an upper bound on the strength of randomization preference for that agent. Notably, data in previous experiments on ambiguity aversion in games is not consistent with a maximal preference for randomization for approximately 30% of subjects.

Suggested Citation

  • Calford, Evan M., 2021. "Mixed strategies and preference for randomization in games with ambiguity averse agents," Journal of Economic Theory, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:jetheo:v:197:y:2021:i:c:s0022053121001435
    DOI: 10.1016/j.jet.2021.105326
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053121001435
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2021.105326?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    2. David Kelsey & Sara Roux, 2015. "An experimental study on the effect of ambiguity in a coordination game," Theory and Decision, Springer, vol. 79(4), pages 667-688, December.
    3. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Preference for Randomisation," Journal of Economic Theory, Elsevier, vol. 71(1), pages 31-43, October.
    4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    5. Bade, Sophie, 2015. "Randomization devices and the elicitation of ambiguity-averse preferences," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 221-235.
    6. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
    7. Eran Hanany & Peter Klibanoff & Sujoy Mukerji, 2020. "Incomplete Information Games with Ambiguity Averse Players," American Economic Journal: Microeconomics, American Economic Association, vol. 12(2), pages 135-187, May.
    8. Calford, Evan M., 2020. "Uncertainty aversion in game theory: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 720-734.
    9. Chen Li & Uyanga Turmunkh & Peter P. Wakker, 2019. "Trust as a decision under ambiguity," Experimental Economics, Springer;Economic Science Association, vol. 22(1), pages 51-75, March.
    10. Shaowei Ke & Qi Zhang, 2020. "Randomization and Ambiguity Aversion," Econometrica, Econometric Society, vol. 88(3), pages 1159-1195, May.
    11. 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.
    12. P. Battigalli & S. Cerreia‐Vioglio & F. Maccheroni & M. Marinacci, 2016. "A Note on Comparative Ambiguity Aversion and Justifiability," Econometrica, Econometric Society, vol. 84, pages 1903-1916, September.
    13. 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.
    14. Ivanov, Asen, 2011. "Attitudes to ambiguity in one-shot normal-form games: An experimental study," Games and Economic Behavior, Elsevier, vol. 71(2), pages 366-394, March.
    15. Kota Saito, 2015. "Preferences for Flexibility and Randomization under Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1246-1271, March.
    16. 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..
    17. Adam Dominiak & Wendelin Schnedler, 2011. "Attitudes toward uncertainty and randomization: an experimental study," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 289-312, October.
    18. Marina Agranov & Pietro Ortoleva, 2017. "Stochastic Choice and Preferences for Randomization," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 40-68.
    19. repec:awi:wpaper:621 is not listed on IDEAS
    20. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    21. Oechssler, Jörg & Rau, Hannes & Roomets, Alex, 2016. "Hedging and Ambiguity," Working Papers 0621, University of Heidelberg, Department of Economics.
    22. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    23. Jonathan Weinstein, 2016. "The Effect of Changes in Risk Attitude on Strategic Behavior," Econometrica, Econometric Society, vol. 84, pages 1881-1902, September.
    24. , G. & , & ,, 2007. "Coarse contingencies and ambiguity," Theoretical Economics, Econometric Society, vol. 2(4), December.
    25. Liu, Zhiwei & Song, Xinxi & Yannelis, Nicholas C., 2020. "Randomization under ambiguity: Efficiency and incentive compatibility," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 1-11.
    26. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
    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. Calford, Evan M., 2020. "Uncertainty aversion in game theory: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 720-734.
    2. Pablo Bra~nas-Garza & Antonio Cabrales & Mar'ia Paz Espinosa & Diego Jorrat, 2022. "The effect of ambiguity in strategic environments: an experiment," Papers 2209.11079, arXiv.org.
    3. le Roux, Sara & Bopp, Fabian, 2025. "Social learning under ambiguity—An experimental study," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 114(C).

    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. Calford, Evan M., 2020. "Uncertainty aversion in game theory: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 720-734.
    2. Evan M. Calford & Gregory DeAngelo, 2023. "Ambiguity and enforcement," Experimental Economics, Springer;Economic Science Association, vol. 26(2), pages 304-338, April.
    3. Christoph Kuzmics & Brian W. Rogers & Xiannong Zhang, 2019. "Is Ellsberg behavior evidence of ambiguity aversion?," Graz Economics Papers 2019-07, University of Graz, Department of Economics.
    4. Li, Chen & Turmunkh, Uyanga & Wakker, Peter P., 2020. "Social and strategic ambiguity versus betrayal aversion," Games and Economic Behavior, Elsevier, vol. 123(C), pages 272-287.
    5. Ghirardato, Paolo & Pennesi, Daniele, 2020. "A general theory of subjective mixtures," Journal of Economic Theory, Elsevier, vol. 188(C).
    6. Kuzmics, Christoph, 2017. "Abraham Wald's complete class theorem and Knightian uncertainty," Games and Economic Behavior, Elsevier, vol. 104(C), pages 666-673.
    7. Calford, Evan, 2016. "Mixed Strategies in Games with Ambiguity Averse Agents," MPRA Paper 74909, University Library of Munich, Germany.
    8. Guarino, Pierfrancesco & Ziegler, Gabriel, 2022. "Optimism and pessimism in strategic interactions under ignorance," Games and Economic Behavior, Elsevier, vol. 136(C), pages 559-585.
    9. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    10. 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.
    11. Christoph Kuzmics & Brian W. Rogers & Xiannong Zhang, 2024. "Randomization advice and ambiguity aversion," Journal of Risk and Uncertainty, Springer, vol. 69(1), pages 85-104, August.
    12. Shaowei Ke & Qi Zhang, 2020. "Randomization and Ambiguity Aversion," Econometrica, Econometric Society, vol. 88(3), pages 1159-1195, May.
    13. Bayer, Péter & Guerdjikova, Ani, 2024. "Optimism leads to optimality: Ambiguity in network formation," Journal of Economic Dynamics and Control, Elsevier, vol. 168(C).
    14. Aurélien Baillon & Yoram Halevy & Chen Li, 2022. "Randomize at Your Own Risk: On the Observability of Ambiguity Aversion," Econometrica, Econometric Society, vol. 90(3), pages 1085-1107, May.
    15. Oechssler, Jörg & Rau, Hannes & Roomets, Alex, 2016. "Hedging and Ambiguity," Working Papers 0621, University of Heidelberg, Department of Economics.
    16. Florian H. Schneider & Martin Schonger, 2019. "An Experimental Test of the Anscombe–Aumann Monotonicity Axiom," Management Science, INFORMS, vol. 65(4), pages 1667-1677, April.
    17. Liu, Zhiwei & Song, Xinxi & Yannelis, Nicholas C., 2020. "Randomization under ambiguity: Efficiency and incentive compatibility," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 1-11.
    18. Cédric Gutierrez & Emmanuel Kemel, 2024. "Measuring natural source dependence," Experimental Economics, Springer;Economic Science Association, vol. 27(2), pages 379-416, April.
    19. Michael Trost, 2014. "On the Equivalence between Iterated Application of Choice Rules and Common Belief of Applying these Rules," Jena Economics Research Papers 2014-032, Friedrich-Schiller-University Jena.
    20. Erick Delage & Daniel Kuhn & Wolfram Wiesemann, 2019. "“Dice”-sion–Making Under Uncertainty: When Can a Random Decision Reduce Risk?," Management Science, INFORMS, vol. 65(7), pages 3282-3301, July.

    More about this item

    Keywords

    Ambiguity aversion; Mixed strategies; Game theory;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:eee:jetheo:v:197:y:2021:i:c:s0022053121001435. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.