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Similarity of differential information with subjective prior beliefs

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  • Khan, M. Ali
  • Sun, Yeneng
  • Tourky, Rabee
  • Zhang, Zhixiang

Abstract

We present a complete, separable and metrizable topology on the product space of information and (subjective) beliefs. Such a topology formalizes similarity of differential information without the assumption of a common prior, but under the assumption that objectively impossible events are considered impossible by subjective beliefs. As an application to the theory of the consumer, we provide results on the continuity of expected utility and demand functions. We also provide continuity results for the value of information and the insurance premium as defined in the literature.

Suggested Citation

  • Khan, M. Ali & Sun, Yeneng & Tourky, Rabee & Zhang, Zhixiang, 2008. "Similarity of differential information with subjective prior beliefs," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 1024-1039, September.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:9-10:p:1024-1039
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    References listed on IDEAS

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    Cited by:

    1. Beißner, Patrick & Khan, M. Ali, 2019. "On Hurwicz–Nash equilibria of non-Bayesian games under incomplete information," Games and Economic Behavior, Elsevier, vol. 115(C), pages 470-490.
    2. Luciana C. Fiorini & José A. Rodrigues-Neto, 2014. "Self-Consistency and Common Prior in Non-Partitional Knowledge Models," ANU Working Papers in Economics and Econometrics 2014-621, Australian National University, College of Business and Economics, School of Economics.
    3. M. Ali Khan & Haomiao Yu & Zhixiang Zhang, 2019. "Information Structures on a General State Space: An Equivalence Theorem and an Application," Working Papers 076, Ryerson University, Department of Economics.
    4. Beissner, Patrick & Tölle, Jonas, 2018. "A Compact Topology for Sigma-Algebra Convergence," Rationality and Competition Discussion Paper Series 74, CRC TRR 190 Rationality and Competition.
    5. Fiorini, Luciana C. & Rodrigues-Neto, José A., 2017. "Self-consistency, consistency and cycles in non-partitional knowledge models," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 11-21.

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