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Agreeing to disagree with generalised decision functions

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  • Tarbush, Bassel
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    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.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 29066.

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    Date of creation: 23 Feb 2011
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    Handle: RePEc:pra:mprapa:29066

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    Related research

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

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    References

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    1. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
    2. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    3. Bonanno, Giacomo & Nehring, Klaus, 1998. "Assessing the truth axiom under incomplete information," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 3-29, July.
    4. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    5. Robert J. Aumann & Sergiu Hart & Motty Perry, 2005. "Conditioning and the Sure-Thing Principle," Discussion Paper Series dp393, The Center for the Study of Rationality, Hebrew University, Jerusalem.
    6. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
    7. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
    8. 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.
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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.

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