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Agreeing to disagree: The non-probabilistic case

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  • Dov Samet

Abstract

A non-probabilistic generalization of Aumann's agreement theorem is proved. Early attempts at such a theorem were based on a version of the sure-thing principle which assumes an intrapersonal-interstate comparison of knowledge. But such comparisons are impossible in partition structures. The theorem proved here is based on a new version of the sure-thing principle that makes an interpersonal-intrastate comparison of knowledge.
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Suggested Citation

  • Dov Samet, 2006. "Agreeing to disagree: The non-probabilistic case," Levine's Bibliography 321307000000000536, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:321307000000000536
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    File URL: http://www.tau.ac.il/~samet/papers/generalized-agreement-theorem.pdf
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    References listed on IDEAS

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    1. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 301-314.
    2. Giacomo Bonanno & Klaus Nehring, "undated". "Agreeing To Disagree: A Survey," Department of Economics 97-18, California Davis - Department of Economics.
    3. 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.
    4. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    5. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
    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. Klaus Nehring, 2003. "Common Priors For Like-Minded Agents," Economics Working Papers 0035, Institute for Advanced Study, School of Social Science.
    8. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
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    Cited by:

    1. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.
    2. Tarbush, Bassel, 2011. "Generalisation of Samet's (2010) agreement theorem," MPRA Paper 29067, University Library of Munich, Germany.
    3. repec:dau:papers:123456789/8575 is not listed on IDEAS
    4. Johan Van Benthem & Eric Pacuit & Olivier Roy, 2011. "Toward a Theory of Play: A Logical Perspective on Games and Interaction," Games, MDPI, vol. 2(1), pages 1-35, February.
    5. Ziv Hellman, 2012. "Deludedly Agreeing to Agree," Discussion Paper Series dp605, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    6. Tarbush, Bassel, 2011. "Agreeing to disagree with generalised decision functions," MPRA Paper 29066, University Library of Munich, Germany.
    7. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    8. Crescenzi, Michele, 2022. "Learning to agree over large state spaces," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    9. Tsakas, Elias & Voorneveld, Mark, 2007. "Efficient communication, common knowledge, and consensus," Working Papers in Economics 255, University of Gothenburg, Department of Economics.
    10. Guarino, Pierfrancesco & Ziegler, Gabriel, 2022. "Optimism and pessimism in strategic interactions under ignorance," Games and Economic Behavior, Elsevier, vol. 136(C), pages 559-585.

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