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Intersubjective Consistency of Beliefs and the Logic of Common Belief

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  • Bonanno, G.
  • Nehring, K.

Abstract

We characterize the class of n-person belief systems for which common belief has the properties of the strongest logic of belief, KD45. The characterizing condition states that individuals are not too mistaken in their beliefs about common beliefs. It is shown to be considerably weaker than the consistency condition on interpersonal beliefs implied by the common knowledge assumption: it allows individuals to ""agree to disagree"" and to be quite incorrect about others7 beliefs.
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Suggested Citation

  • Bonanno, G. & Nehring, K., 1995. "Intersubjective Consistency of Beliefs and the Logic of Common Belief," Department of Economics 95-08, California Davis - Department of Economics.
    • Handle: RePEc:fth:caldec:95-08
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    References listed on IDEAS

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    1. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    2. LISMONT, Luc & MONGIN, Philippe, 1994. "On the Logic of Common Belief and Common Knowledge," LIDAM Discussion Papers CORE 1994005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Milgrom, Paul, 1981. "An Axiomatic Characterization of Common Knowledge," Econometrica, Econometric Society, vol. 49(1), pages 219-222, January.
    4. 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.
    5. Shin Hyun Song, 1993. "Logical Structure of Common Knowledge," Journal of Economic Theory, Elsevier, vol. 60(1), pages 1-13, June.
    6. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    7. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    8. Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
    9. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    10. Bonanno, G., 1994. "The Logic of Shared Belief, Public Rumor, Public Shared Belief and Common Belief," Papers 94-10, California Davis - Institute of Governmental Affairs.
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    More about this item

    Keywords

    MATHEMATICS;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D10 - Microeconomics - - Household Behavior - - - General
    • D19 - Microeconomics - - Household Behavior - - - Other

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