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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- Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
- Samet, Dov, 2000.
"Quantified Beliefs and Believed Quantities,"
Journal of Economic Theory,
Elsevier, vol. 95(2), pages 169-185, December.
- MONGINÂ , 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).
- Dov Samet, 1997. "On the Triviality of High-Order Probabilistic Beliefs," Game Theory and Information 9705001, EconWPA.
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