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Ambiguity Attitudes and Self-Confirming Equilibrium in Sequential Games

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  • Pierpaolo Battigalli
  • Emiliano Catonini
  • Giacomo Lanzani
  • Massimo Marinacci

Abstract

We consider a game with sequential moves played by agents who are randomly drawn from large populations and matched. We assume that, when players are uncertain about the strategy distributions of the opponents, preferences over actions at any information set admit a smooth-ambiguity representation in the sense of Klibanoff, Marinacci, and Mukerji (Econometrica, 2005). This may induce dynamically inconsistent preferences and calls for an appropriate definition of sequential best response. We take this into account in our analysis of self-confirming equilibrium (SCE) and rationalizable SCE in sequential games with feedback played by agents with non-neutral ambiguity attitudes. Battigalli, Cerreia-Vioglio, Maccheroni, and Marinacci (Amer. Econ. Rev., 2015) show that the set of SCE's of a simultaneous-move game with feedback expands as ambiguity aversion increases. We show by example that SCE in a sequential game is not equivalent to SCE applied to the strategic form of such game, and that the previous monotonicity result does not extend to general sequential games. Still, we provide sufficient conditions under which the monotonicity result holds for (rationalizable) SCE. Keywords: Sequential games with feedback, smooth ambiguity, self-confirming equilibrium, rationalizable self-confirming equilibrium.

Suggested Citation

  • Pierpaolo Battigalli & Emiliano Catonini & Giacomo Lanzani & Massimo Marinacci, 2017. "Ambiguity Attitudes and Self-Confirming Equilibrium in Sequential Games," Working Papers 607, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:607
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    Cited by:

    1. 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.
    2. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    3. Beggs, Alan, 2021. "Games with second-order expected utility," Games and Economic Behavior, Elsevier, vol. 130(C), pages 569-590.
    4. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    5. 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.
    6. Sebastiano Della Lena & Fabrizio Panebianco, 2019. "Cultural Transmission with Incomplete Information: Parental Perceived Efficacy and Group Misrepresentation," Working Papers 2019:11, Department of Economics, University of Venice "Ca' Foscari".
    7. Tommi Ekholm & Erin Baker, 2022. "Multiple Beliefs, Dominance and Dynamic Consistency," Management Science, INFORMS, vol. 68(1), pages 529-540, January.
    8. Battigalli, Pierpaolo & Generoso, Nicolò, 2024. "Information flows and memory in games," Games and Economic Behavior, Elsevier, vol. 145(C), pages 356-376.
    9. Spyros Galanis & Christos A Ioannou & Stelios Kotronis, 2024. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(6), pages 3423-3467.
    10. Battigalli, P. & Francetich, A. & Lanzani, G. & Marinacci, M., 2019. "Learning and self-confirming long-run biases," Journal of Economic Theory, Elsevier, vol. 183(C), pages 740-785.
    11. Pierpaolo Battigalli & Davide Bordoli, 2023. "Sophisticated Reasoning, Learning, and Equilibrium in Repeated Games with Imperfect Feedback," Working Papers 702, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    12. Auster, Sarah & Kellner, Christian, 2022. "Robust bidding and revenue in descending price auctions," Journal of Economic Theory, Elsevier, vol. 199(C).
    13. Chen, Jaden Yang, 2022. "Biased learning under ambiguous information," Journal of Economic Theory, Elsevier, vol. 203(C).
    14. 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.

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    More about this item

    Keywords

    sequential games with feedback; smooth ambiguity; self-confirming equilibrium; rationalizable self-confirming equilibrium.;
    All these keywords.

    JEL classification:

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

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