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The Epistemic Spirit of Divinity

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  • Pierpaolo Battigalli
  • Emiliano Catonini

Abstract

We study strategic reasoning in a signaling game where players have common belief in an outcome distribution and in the event that the receiver believes that the sender's first-order beliefs are independent of her payoff-type. We characterize the behavioral implications of these epistemic hypotheses through a rationalizability procedure with second-order belief restrictions. Our solution concept is related to, but weaker than Divine Equilibrium (Banks and Sobel, 1987). First, we do not obtain sequential equilibrium, but just Perfect Bayesian Equilibrium with heterogeneous off-path beliefs (Fudenberg and He, 2018). Second, when we model how the receiver may rationalize a particular deviation, we take into account that some types could have preferred a different deviation, and we show this is natural and relevant via an economic example.

Suggested Citation

  • Pierpaolo Battigalli & Emiliano Catonini, 2022. "The Epistemic Spirit of Divinity," Working Papers 681, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:681
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    References listed on IDEAS

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    1. Emiliano Catonini, 2022. "A Dutch book argument for belief consistency," Papers 2202.10121, arXiv.org.
    2. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    3. 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..
    4. , & ,, 2015. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, vol. 10(3), September.
    5. Battigalli Pierpaolo & Prestipino Andrea, 2013. "Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 79-130, May.
    6. Drew Fudenberg & Kevin He, 2018. "Learning and Type Compatibility in Signaling Games," Econometrica, Econometric Society, vol. 86(4), pages 1215-1255, July.
    7. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    8. Emiliano Catonini, 2021. "Self-enforcing Agreements and Forward Induction Reasoning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(2), pages 610-642.
    9. Battigalli, P. & Catonini, E. & Manili, J., 2023. "Belief change, rationality, and strategic reasoning in sequential games," Games and Economic Behavior, Elsevier, vol. 142(C), pages 527-551.
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