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An infinitary probability logic for type spaces

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Author Info
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.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2001061.

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Date of creation: 01 Dec 2001
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Handle: RePEc:cor:louvco:2001061

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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.:
  1. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April. [Downloadable!] (restricted)
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  2. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October. [Downloadable!] (restricted)
  3. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February. [Downloadable!] (restricted)
  4. Heifetz, Aviad & Samet, Dov, 1999. "Coherent beliefs are not always types," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 475-488, December. [Downloadable!] (restricted)
  5. MERTENSÊ, Jean-Franois & SORINÊ, Sylvain & ZAMIRÊ, Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Heifetz, Aviad, 1993. "The Bayesian Formulation of Incomplete Information--The Non-compact Case," International Journal of Game Theory, Springer, vol. 21(4), pages 329-338.
  7. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300. [Downloadable!] (restricted)
  8. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314. [Downloadable!] (restricted)
  9. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Shmuel Zamir, 2008. "Bayesian games: games of incomplete information," Levine's Bibliography 122247000000002215, UCLA Department of Economics. [Downloadable!]
  2. Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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