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Probability Logic for Type Spaces

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  • Heifetz, Aviad
  • Mongin, Philippe

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.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 35 (2001)
Issue (Month): 1-2 (April)
Pages: 31-53

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Handle: RePEc:eee:gamebe:v:35:y:2001:i:1-2:p:31-53

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Dov Samet, 1998. "Quantified beliefs and believed quantities," Game Theory and Information 9805003, EconWPA.
  2. Dov Samet, 1997. "On the Triviality of High-Order Probabilistic Beliefs," Game Theory and Information 9705001, EconWPA.
  3. 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).
  4. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
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Citations

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Cited by:
  1. Mongin, Philippe, 2011. "Judgment aggregation," Les Cahiers de Recherche 942, HEC Paris.
  2. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
  3. Pintér, Miklós, 2010. "The non-existence of a universal topological type space," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 223-229, March.
  4. Mongin, Philippe, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," MPRA Paper 37752, University Library of Munich, Germany.
  5. Dietrich, Franz & Mongin Philippe, 2008. "The Premiss-Based Approach to Judgment Aggregation," Research Memorandum 013, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Pintér, Miklós, 2011. "Common priors for generalized type spaces," MPRA Paper 44818, University Library of Munich, Germany.
  7. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," Les Cahiers de Recherche 941, HEC Paris.
  8. 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).
  9. Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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