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Probability Logic for Type Spaces

Author

Listed:
  • Heifetz, A.
  • Mongin, P.

Abstract

Using a formal propositional language with operators "individual i assigns probability at least a" for countable many a, we devise an axiom system which is sound and complete with respect to the class of type spaces in the sense of Harsanyi (1967-68). A crucial axiom requires that degrees of belief be compatible for any two sets of assertions which are equivalent in a suitably defined natural sense. The completeness proof relies on a theorem of the alternative from convex analysis, and uses the method of filtration by finite sub-languages.

Suggested Citation

  • Heifetz, A. & Mongin, P., 1998. "Probability Logic for Type Spaces," Papers 9825, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  • Handle: RePEc:fth:pnegmi:9825
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    References listed on IDEAS

    as
    1. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
    2. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 301-314.
    3. Dov Samet, 1997. "On the Triviality of High-Order Probabilistic Beliefs," Game Theory and Information 9705001, EconWPA.
    4. MONGIN , Philippe, 1993. "A Non-Minimal but Very Weak Axiomatization of Common Belief," CORE Discussion Papers 1993046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Citations

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    Cited by:

    1. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    2. Tsakas, Elias, 2014. "Rational belief hierarchies," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 121-127.
    3. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    4. Di Tillio, Alfredo & Halpern, Joseph Y. & Samet, Dov, 2014. "Conditional belief types," Games and Economic Behavior, Elsevier, vol. 87(C), pages 253-268.
    5. Philippe Mongin & Franz Dietrich, 2011. "An Interpretive Account of Logical Aggregation Theory," Working Papers hal-00625427, HAL.
    6. repec:spr:etbull:v:2:y:2014:i:2:d:10.1007_s40505-014-0037-5 is not listed on IDEAS
    7. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
    8. Philippe Mongin, 2011. "Judgment aggregation," Working Papers hal-00579346, HAL.
    9. Pintér, Miklós, 2011. "Common priors for generalized type spaces," MPRA Paper 34118, University Library of Munich, Germany.
    10. Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    11. Pintér, Miklós, 2010. "The non-existence of a universal topological type space," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 223-229, March.
    12. MEIER, Martin, 2001. "An infinitary probability logic for type spaces," CORE Discussion Papers 2001061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.
    14. Meier, Martin, 2008. "Universal knowledge-belief structures," Games and Economic Behavior, Elsevier, vol. 62(1), pages 53-66, January.
    15. Mikaël Cozic, 2016. "Probabilistic Unawareness," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-24, November.
    16. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

    More about this item

    Keywords

    PROBABILITY;

    JEL classification:

    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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