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Agreeing to disagree with generalised decision functions

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  • Tarbush, Bassel

Abstract

We develop a framework that allows us to emulate standard results from the “agreeing to disagree" literature with generalised decision functions (e.g. Bacharach (1985)) in a manner the avoids known incoherences pointed out by Moses and Nachum (1990). We analyse the implications of the Sure-Thing Principle, a central assumption. The upshot is that the way in which states are described matters, and that the results fail if decisions are allowed to depend on interactive information. Furthermore, using very weak additional assumptions, we extend all previous results to models with a non-partitional information structure in a coherent manner. Finally, we provide agreement theorems in which the decision functions are not required to satisfy the Sure-Thing Principle.

Suggested Citation

  • Tarbush, Bassel, 2011. "Agreeing to disagree with generalised decision functions," MPRA Paper 29066, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:29066
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    File URL: https://mpra.ub.uni-muenchen.de/32076/2/MPRA_paper_32076.pdf
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    References listed on IDEAS

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    1. 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.
    2. Bonanno, Giacomo & Nehring, Klaus, 1998. "Assessing the truth axiom under incomplete information," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 3-29, July.
    3. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    4. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    5. Robert J. Aumann & Sergiu Hart & Motty Perry, 2005. "Conditioning and the Sure-Thing Principle," Discussion Paper Series dp393, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    6. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    7. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
    8. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    9. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
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    Cited by:

    1. Tarbush, Bassel, 2011. "Generalisation of Samet's (2010) agreement theorem," MPRA Paper 29067, University Library of Munich, Germany.

    More about this item

    Keywords

    Agreeing to disagree; knowledge; common knowledge; belief; information; epistemic logic;

    JEL classification:

    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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