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"Agreeing to Disagree" Type Results under Ambiguity

  • Lefort, Jean-Philippe
  • Dominiak, Adam
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    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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    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
    Contact details of provider: Web page: http://www.dauphine.fr/en/welcome.html

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    1. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    2. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    3. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    5. Jiankang Zhang, 2002. "Subjective ambiguity, expected utility and Choquet expected utility," Economic Theory, Springer, vol. 20(1), pages 159-181.
    6. Milgrom, Paul, 1981. "An Axiomatic Characterization of Common Knowledge," Econometrica, Econometric Society, vol. 49(1), pages 219-22, January.
    7. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    8. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
    9. 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.
    10. Klibanoff, Peter & Hanany, Eran, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    11. Halevy, Yoram, 2004. "The possibility of speculative trade between dynamically consistent agents," Games and Economic Behavior, Elsevier, vol. 46(1), pages 189-198, January.
    12. Klaus Nehring & Michael Magill & Julian R. Betts, 2003. "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Working Papers 978, University of California, Davis, Department of Economics.
    13. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
    14. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    15. 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.
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