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An infinitary probability logic for type spaces

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  • MEIER, Martin

Abstract

Type spaces in the sense of Harsanyi (1967/68) can be considered as the probabilistic analog of Kripke structures. By an infinitary propositional language with additional operators "individual i assigns probability at least to" and infinitary inference rules, we axiomatize the class of (Harsanyi) type spaces. We show that our axiom system is strongly sound and strongly complete. To the best of our knowledge, this is the very first strong completeness theorem for a probability logic of the present kind. The result is proved by constructing a canonical type space.

Suggested Citation

  • MEIER, Martin, 2001. "An infinitary probability logic for type spaces," LIDAM Discussion Papers CORE 2001061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2001061
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    Cited by:

    1. 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.
    2. Pintér, Miklós, 2010. "The non-existence of a universal topological type space," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 223-229, March.
    3. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.

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