IDEAS home Printed from https://ideas.repec.org/a/aea/aejmic/v12y2020i2p135-87.html
   My bibliography  Save this article

Incomplete Information Games with Ambiguity Averse Players

Author

Listed:
  • Eran Hanany
  • Peter Klibanoff
  • Sujoy Mukerji

Abstract

We study incomplete information games with ambiguity averse players. Our focus is on equilibrium concepts satisfying sequential optimality—each player's strategy is optimal at each information set given opponents' strategies. We show sequential optimality, which does not make any explicit assumption on updating, is equivalent to sequential optimality with respect to beliefs updated using a particular generalization of Bayesian updating. Ambiguity aversion expands the set of equilibria compatible with players sharing common ambiguous beliefs. We connect ambiguity aversion with belief robustness. Examples illustrate new strategic behavior, including strategic use of ambiguity, under ambiguity aversion.

Suggested Citation

  • 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.
    • Handle: RePEc:aea:aejmic:v:12:y:2020:i:2:p:135-87
    DOI: 10.1257/mic.20180302
    as

    Download full text from publisher

    File URL: https://www.aeaweb.org/doi/10.1257/mic.20180302
    Download Restriction: no
    File URL: https://www.aeaweb.org/doi/10.1257/mic.20180302.appx
    Download Restriction: no
    File URL: https://www.aeaweb.org/doi/10.1257/mic.20180302.ds
    Download Restriction: Access to full text is restricted to AEA members and institutional subscribers.
    File URL: https://libkey.io/10.1257/mic.20180302?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sandeep Baliga & Eran Hanany & Peter Klibanoff, 2013. "Polarization and Ambiguity," American Economic Review, American Economic Association, vol. 103(7), pages 3071-3083, December.
    2. Lars Peter Hansen & Thomas J Sargent, 2014. "Beliefs, Doubts and Learning: Valuing Macroeconomic Risk," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 10, pages 331-377, World Scientific Publishing Co. Pte. Ltd..
    3. Mehdi Ayouni & Frédéric Koessler, 2017. "Hard evidence and ambiguity aversion," Theory and Decision, Springer, vol. 82(3), pages 327-339, March.
    4. Jürgen Eichberger & David Kelsey, 2004. "Sequential Two-Player Games With Ambiguity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1229-1261, November.
    5. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    6. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016057.
    7. Alfredo Di Tillio & Nenad Kos & Matthias Messner, 2012. "The Design of Ambiguous Mechanisms," Working Papers 446, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    8. Milgrom, Paul & Roberts, John, 1982. "Limit Pricing and Entry under Incomplete Information: An Equilibrium Analysis," Econometrica, Econometric Society, vol. 50(2), pages 443-459, March.
    9. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    10. Paolo Ghirardato & Marciano Siniscalchi, 2012. "Ambiguity in the Small and in the Large," Econometrica, Econometric Society, vol. 80(6), pages 2827-2847, November.
    11. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, vol. 71(2), pages 246-260, March.
    12. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    13. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    14. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    15. Auster, Sarah, 2018. "Robust contracting under common value uncertainty," Theoretical Economics, Econometric Society, vol. 13(1), January.
    16. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    17. repec:oup:restud:v:84:y::i:1:p:237-276. is not listed on IDEAS
    18. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.
    19. ,, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    20. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    21. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    22. Perea, Andres, 2002. "A note on the one-deviation property in extensive form games," Games and Economic Behavior, Elsevier, vol. 40(2), pages 322-338, August.
    23. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107674165.
    24. , & ,, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    25. Alfredo di Tillio & Nenad Kos & Matthias Messner, 2017. "The Design of Ambiguous Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(1), pages 237-276.
    26. Kellner, Christian & Le Quement, Mark T., 2017. "Modes of ambiguous communication," Games and Economic Behavior, Elsevier, vol. 104(C), pages 271-292.
    27. Muraviev, Igor & Riedel, Frank & Sass, Linda, 2017. "Kuhn’s Theorem for extensive form Ellsberg games," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 26-41.
    28. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    29. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016064.
    30. Bose, Subir & Daripa, Arup, 2009. "A dynamic mechanism and surplus extraction under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2084-2114, September.
    31. Pahlke, Marieke, 2018. "Dynamic Consistency in Incomplete Information Games with Multiple Priors," Center for Mathematical Economics Working Papers 599, Center for Mathematical Economics, Bielefeld University.
    32. Itzhak Gilboa, 2004. "Uncertainty in Economic Theory," Post-Print hal-00756317, HAL.
    33. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    34. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107627314.
    35. Joseph Greenberg, 2000. "The Right to Remain Silent," Theory and Decision, Springer, vol. 48(2), pages 193-204, March.
    36. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016040.
    37. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    38. Chen, Yan & Katuscak, Peter & Ozdenoren, Emre, 2007. "Sealed bid auctions with ambiguity: Theory and experiments," Journal of Economic Theory, Elsevier, vol. 136(1), pages 513-535, September.
    39. Hanany Eran & Klibanoff Peter, 2009. "Updating Ambiguity Averse Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-53, November.
    40. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "The One-Shot-Deviation Principle for Sequential Rationality," Games and Economic Behavior, Elsevier, vol. 12(2), pages 274-282, February.
    41. Battigalli, P. & Catonini, E. & Lanzani, G. & Marinacci, M., 2019. "Ambiguity attitudes and self-confirming equilibrium in sequential games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 1-29.
    42. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    43. Bodoh-Creed, Aaron L., 2012. "Ambiguous beliefs and mechanism design," Games and Economic Behavior, Elsevier, vol. 75(2), pages 518-537.
    44. Kuzmics, Christoph, 2017. "Abraham Wald's complete class theorem and Knightian uncertainty," Games and Economic Behavior, Elsevier, vol. 104(C), pages 666-673.
    45. Levin, Dan & Ozdenoren, Emre, 2004. "Auctions with uncertain numbers of bidders," Journal of Economic Theory, Elsevier, vol. 118(2), pages 229-251, October.
    46. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
    47. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    48. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107638105.
    49. Salo, Ahti A & Weber, Martin, 1995. "Ambiguity Aversion in First-Price Sealed-Bid Auctions," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 123-137, September.
    50. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    51. Kellner, Christian, 2015. "Tournaments as a response to ambiguity aversion in incentive contracts," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 627-655.
    52. Lars Peter Hansen, 2007. "Beliefs, Doubts and Learning: Valuing Economic Risk," NBER Working Papers 12948, National Bureau of Economic Research, Inc.
    53. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
    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. Beggs, Alan, 2021. "Games with second-order expected utility," Games and Economic Behavior, Elsevier, vol. 130(C), pages 569-590.
    2. Auster, Sarah & Kellner, Christian, 2022. "Robust bidding and revenue in descending price auctions," Journal of Economic Theory, Elsevier, vol. 199(C).
    3. Laohakunakorn, Krittanai & Levy, Gilat & Razin, Ronny, 2019. "Private and common value auctions with ambiguity over correlation," Journal of Economic Theory, Elsevier, vol. 184(C).
    4. Gerrit Bauch & Frank Riedel, 2022. "The Texas Shootout under Uncertainty," Papers 2211.10089, arXiv.org.
    5. Kishishita, Daiki, 2020. "(Not) delegating decisions to experts: The effect of uncertainty," Journal of Economic Theory, Elsevier, vol. 190(C).
    6. Yang Hao, 2023. "Financial Market with Learning from Price under Knightian Uncertainty," Working Papers hal-03686748, HAL.
    7. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    8. Spyros Galanis, 2021. "Dynamic consistency, valuable information and subjective beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1467-1497, June.
    9. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    10. Richard J. Arend, 2022. "Strategic decision-making under ambiguity: insights from exploring a simple linked two-game model," Operational Research, Springer, vol. 22(5), pages 5845-5861, November.
    11. Battigalli, P. & Catonini, E. & Lanzani, G. & Marinacci, M., 2019. "Ambiguity attitudes and self-confirming equilibrium in sequential games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 1-29.
    12. Brishti Guha, 2020. "Revisiting the volunteer's dilemma: group size and public good provision in the presence of some ambiguity aversion," Economics Bulletin, AccessEcon, vol. 40(2), pages 1308-1318.
    13. Pahlke, Marieke, 2018. "Dynamic Consistency in Incomplete Information Games with Multiple Priors," Center for Mathematical Economics Working Papers 599, Center for Mathematical Economics, Bielefeld University.
    14. Colo, Philippe, 2021. "Expert-based Knowledge: Communicating over Scientific Models," MPRA Paper 110434, University Library of Munich, Germany.
    15. Calford, Evan M., 2021. "Mixed strategies and preference for randomization in games with ambiguity averse agents," Journal of Economic Theory, Elsevier, vol. 197(C).
    16. Xiaoyu Cheng, 2020. "Ambiguous Persuasion: An Ex-Ante Formulation," Papers 2010.05376, arXiv.org, revised Nov 2023.
    17. Laohakunakorn, Krittanai & Levy, Gilat & Razin, Ronny, 2019. "Private and common value auctions with ambiguity over correlation," LSE Research Online Documents on Economics 101410, London School of Economics and Political Science, LSE Library.
    18. Evan M. Calford & Gregory DeAngelo, 2023. "Ambiguity and enforcement," Experimental Economics, Springer;Economic Science Association, vol. 26(2), pages 304-338, April.

    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. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Beauchêne, Dorian & Li, Jian & Li, Ming, 2019. "Ambiguous persuasion," Journal of Economic Theory, Elsevier, vol. 179(C), pages 312-365.
    3. Massimo Marinacci, 2015. "Model Uncertainty," Journal of the European Economic Association, European Economic Association, vol. 13(6), pages 1022-1100, December.
    4. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    5. Auster, Sarah & Kellner, Christian, 2022. "Robust bidding and revenue in descending price auctions," Journal of Economic Theory, Elsevier, vol. 199(C).
    6. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    7. Dominiak, Adam & Eichberger, Jürgen, 2021. "Games in context: Equilibrium under ambiguity for belief functions," Games and Economic Behavior, Elsevier, vol. 128(C), pages 125-159.
    8. Takashi Ui, 2021. "Strategic Ambiguity in Global Games," Working Papers on Central Bank Communication 032, University of Tokyo, Graduate School of Economics.
    9. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    10. Bade, Sophie, 2022. "Dynamic semi-consistency," Games and Economic Behavior, Elsevier, vol. 134(C), pages 117-126.
    11. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
    12. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    13. Gaurab Aryal & Ronald Stauber, 2014. "Trembles in extensive games with ambiguity averse players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(1), pages 1-40, September.
    14. Dominiak, Adam & Duersch, Peter, 2015. "Benevolent and Malevolent Ellsberg Games," Working Papers 0592, University of Heidelberg, Department of Economics.
    15. Massimiliano Amarante, 2017. "Information and Ambiguity: Toward a Foundation of Nonexpected Utility," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1254-1279, November.
    16. Loic Berger & Massimo Marinacci, 2017. "Model Uncertainty in Climate Change Economics," Working Papers 616, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    18. Loïc Berger & Massimo Marinacci, 2020. "Model Uncertainty in Climate Change Economics: A Review and Proposed Framework for Future Research," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 77(3), pages 475-501, November.
    19. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo, 2022. "Ambiguity aversion and wealth effects," Journal of Economic Theory, Elsevier, vol. 199(C).
    20. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:aea:aejmic:v:12:y:2020:i:2:p:135-87. 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: Michael P. Albert (email available below). General contact details of provider: https://edirc.repec.org/data/aeaaaea.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.