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"Agreeing to Disagree" Type Results under Ambiguity

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  • Lefort, Jean-Philippe
  • Dominiak, Adam
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    Abstract

    In this paper we show that unlike in Bayesian frameworks asymmetric information does matter and can explain differences in common knowledge decisions due to ambiguous character of agents' private information. Agents share a common-but-not-necessarily-additive prior beliefs represented by capacities. It is shown that, if each agent's information partition is made up of unambiguous events in the sense of Nehring (1999, Mat. Soc. Sci. 38, 197-213), then it is impossible that the agents disagree on their commonly known decisions, whatever these decisions are : whether posterior beliefs or conditional expectations. Conversely, an agreement on conditional expectations, but not on posterior beliefs, implies that agents' private information must consist of Nehring-unambiguous events. The results obtained allow to attribute the existence of a speculative trade to the presence of agents' diverse and ambiguous information.

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    File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/8575/3/K_Agreement_under_Ambiguity_16_8.pdf
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    Bibliographic Info

    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/8575.

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    Date of creation: 2011
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    Publication status: Published in TARK XIII : Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge,
    Handle: RePEc:dau:papers:123456789/8575

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    Related research

    Keywords: capacities; Ambiguity; No-Trade Theorem; Choquet expected utility theory; unambiguous events; Agreement Theorem; common knowledge; asymmetric information;

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    1. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
    2. Nakamura, Yutaka, 1990. "Subjective expected utility with non-additive probabilities on finite state spaces," Journal of Economic Theory, Elsevier, vol. 51(2), pages 346-366, August.
    3. Halevy, Yoram, 2004. "The possibility of speculative trade between dynamically consistent agents," Games and Economic Behavior, Elsevier, vol. 46(1), pages 189-198, January.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
    5. Rubinstein, Ariel & Wolinsky, Asher, 1990. "On the logic of "agreeing to disagree" type results," Journal of Economic Theory, Elsevier, vol. 51(1), pages 184-193, June.
    6. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
    7. Milgrom, Paul, 1981. "An Axiomatic Characterization of Common Knowledge," Econometrica, Econometric Society, vol. 49(1), pages 219-22, January.
    8. Dov Samet, 2006. "Agreeing to disagree: The non-probabilistic case," Levine's Bibliography 321307000000000536, UCLA Department of Economics.
    9. Jiankang Zhang, 1999. "Subjective Ambiguity, Expected Utility and Choquet Expected Utility," Carleton Economic Papers 99-19, Carleton University, Department of Economics, revised Aug 2002.
    10. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    11. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
    12. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    13. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    14. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    15. Klibanoff, Peter & Hanany, Eran, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
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