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Charges and Bets: A General Characterisation of Common Priors

Author

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  • Ziv Hellman

    (Bar-Ilan University)

  • Miklós Pintér

Abstract

The seminal no betting theorem on the equivalence of common priors and absence of agreeable bets obtains only over compact state spaces. We show here that this equivalence can be generalised to any infinite space if we expand the set of priors to include probability charges as priors. Going beyond the strict prior/no common prior dichotomy, we further uncover a fine-grained decomposition of the space of type spaces into continuum many subclasses in each of which an epistemic condition approximating common priors is equivalent to a behavioural condition limiting acceptable bets. Several additional concepts relating to approximations of common priors and type spaces admitting common priors are studied, elucidating more aspects of the structure of the class of type spaces.

Suggested Citation

  • Ziv Hellman & Miklós Pintér, 2020. "Charges and Bets: A General Characterisation of Common Priors," Working Papers 2020-06, Bar-Ilan University, Department of Economics.
    • Handle: RePEc:biu:wpaper:2020-06
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    References listed on IDEAS

    as
    1. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    2. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    3. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 399-410, May.
    4. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.
    5. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Common prior; no betting; probability charge;
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