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Agreeable Bets with Multiple Priors

Author

Listed:
  • Atsushi Kajii

    (Institute of Economic Research, Kyoto University)

  • Takashi Ui

    (Faculty of Economics, Yokohama National University)

Abstract

This paper considers a two agent model of trade with multiple priors. First, we characterize the existence of an agreeable bet on some event in terms of the set of priors. It is then shown that the existence of an agreeable bet on some event is a strictly stronger condition than the existence of an agreeable trade, whereas the two conditions are equivalent in the standard Bayesian framework. Secondly, we show that the two conditions are equivalent when the set of priors is the core of a convex capacity.

Suggested Citation

  • Atsushi Kajii & Takashi Ui, 2004. "Agreeable Bets with Multiple Priors," KIER Working Papers 581, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:581
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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP581.pdf
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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. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, pages 685-694.
    3. Tallon, Jean-Marc, 1998. "Do sunspots matter when agents are Choquet-expected-utility maximizers?," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 357-368, March.
    4. Kajii, Atsushi & Ui, Takashi, 2006. "Agreeable bets with multiple priors," Journal of Economic Theory, Elsevier, pages 299-305.
    5. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    6. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallou, 2002. "Sharing beliefs and the absence of betting in the Choquet expected utility model," Statistical Papers, Springer, pages 127-136.
    9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    10. Denneberg, Dieter, 2002. "Conditional expectation for monotone measures, the discrete case," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 105-121, April.
    11. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Dana, R.A. & Le Van, C., 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2186-2202, November.
    2. Dominiak, Adam & Eichberger, Jürgen & Lefort, Jean-Philippe, 2012. "Agreeable trade with optimism and pessimism," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 119-126.
    3. repec:eee:mateco:v:70:y:2017:i:c:p:115-122 is not listed on IDEAS
    4. Rose-Anne Dana & Cuong Le Van, 2008. "No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity," Documents de travail du Centre d'Economie de la Sorbonne b08039, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.
    5. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    6. Strzalecki, Tomasz & Werner, Jan, 2011. "Efficient allocations under ambiguity," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1173-1194, May.
    7. repec:hal:journl:halshs-00281582 is not listed on IDEAS
    8. Faias, Marta & Torres-Martínez, Juan Pablo, 2017. "Credit market segmentation, essentiality of commodities, and supermodularity," Journal of Mathematical Economics, Elsevier, pages 115-122.
    9. Kajii, Atsushi & Ui, Takashi, 2006. "Agreeable bets with multiple priors," Journal of Economic Theory, Elsevier, pages 299-305.
    10. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
    11. Tian, Dejian & Tian, Weidong, 2014. "Optimal risk-sharing under mutually singular beliefs," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 41-49.

    More about this item

    Keywords

    multiple priors; convex capacity; agreeing and disagreeing; Choquet integralm;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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