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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 9-10 (September)
Pages: 1024-1039

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Handle: RePEc:eee:mateco:v:44:y:2008:i:9-10:p:1024-1039

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Web page: http://www.elsevier.com/locate/jmateco

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  1. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer, vol. 28(3), pages 409-434.
  2. Cotter, Kevin D., 1991. "Similarity of games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 501-520.
  3. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-78, May.
  4. Ali Khan, M. & Rustichini, Aldo, 1993. "Cournot-Nash equilibrium distributions of games with uncertainty and imperfect information," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 35-59.
  5. Jordan, James S. & Radner, Roy, 1982. "Rational expectations in microeconomic models: An overview," Journal of Economic Theory, Elsevier, vol. 26(2), pages 201-223, April.
  6. Cotter, Kevin D., 1987. "Convergence of information, random variables and noise," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 39-51, February.
  7. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2003. "On The Continuity Of Equilibrium And Core Correspondences In Economies With Differential Information," Economics Working Papers we032707, Universidad Carlos III, Departamento de Economía.
  8. João Correia-da-Silva & Carlos Hervés-Beloso, 2007. "Private Information: Similarity as Compatibility," Economic Theory, Springer, vol. 30(3), pages 395-407, March.
  9. M Ali Khan & Yeneng Sun, 2002. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 482, The Johns Hopkins University,Department of Economics.
  10. Joseph Y. Halpern, 2000. "Characterizing the Common Prior Assumption," Game Theory and Information 0004009, EconWPA.
  11. Stinchcombe, Maxwell B., 1993. "A further note on Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 22(2), pages 189-193.
  12. Roy Radner, 1997. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Levine's Working Paper Archive 1594, David K. Levine.
  13. Allen, Beth, 1983. "Neighboring information and distributions of agents' characteristics under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 63-101, September.
  14. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
  15. Van Zandt, Timothy, 2002. "Information, measurability, and continuous behavior," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 293-309, November.
  16. Cotter, Kevin D., 1986. "Similarity of information and behavior with a pointwise convergence topology," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 25-38, February.
  17. Allen, Beth, 1986. "The Demand for (Differentiated) Information," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 311-23, July.
  18. Yannelis, Nicholas C, 1991. "The Core of an Economy with Differential Information," Economic Theory, Springer, vol. 1(2), pages 183-97, April.
  19. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
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