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Ambiguity Attitudes and Self-Confi rming 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 inconsis- tent preferences and calls for an appropriate defi nition of sequential best response. We take this into account in our analysis of self-con firming 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 SCEs 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-confi rming equilibrium, rationalizable self-confi rming equilibrium.

Suggested Citation

  • Pierpaolo Battigalli & Emiliano Catonini & Giacomo Lanzani & Massimo Marinacci, 2017. "Ambiguity Attitudes and Self-Confi rming 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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    References listed on IDEAS

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    1. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
    2. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 1999. "Payoff Information and Self-Confirming Equilibrium," Journal of Economic Theory, Elsevier, vol. 89(2), pages 165-185, December.
    3. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    4. Kamada, Yuichiro & Fudenberg, Drew, 2015. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, vol. 10(3), September.
    5. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February.
    6. Lawrence Blume & David Easley, 2006. "If You're so Smart, why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, vol. 74(4), pages 929-966, July.
    7. Esponda, Ignacio, 2013. "Rationalizable conjectural equilibrium: A framework for robust predictions," Theoretical Economics, Econometric Society, vol. 8(2), May.
    8. Massimo Marinacci, 2015. "Model Uncertainty," Journal of the European Economic Association, European Economic Association, vol. 13(6), pages 1022-1100, December.
    9. 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.
    10. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
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