Probability Logic for Type Spaces
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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|Date of creation:||1998|
|Contact details of provider:|| Postal: THEMA, Universite de Paris X-Nanterre, U.F.R. de science economiques, gestion, mathematiques et informatique, 200, avenue de la Republique 92001 Nanterre CEDEX.|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Samet, Dov, 2000.
"Quantified Beliefs and Believed Quantities,"
Journal of Economic Theory,
Elsevier, vol. 95(2), pages 169-185, December.
- Dov Samet, 1998. "Quantified beliefs and believed quantities," Game Theory and Information 9805003, EconWPA.
- Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 301-314.
- Dov Samet, 1997. "On the Triviality of High-Order Probabilistic Beliefs," Game Theory and Information 9705001, EconWPA.
- 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). Full references (including those not matched with items on IDEAS)