IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v44y2008i9-10p1024-1039.html
   My bibliography  Save this article

Similarity of differential information with subjective prior beliefs

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(07)00123-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stinchcombe, Maxwell B., 1993. "A further note on Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 22(2), pages 189-193.
    2. Yannelis, Nicholas C, 1991. "The Core of an Economy with Differential Information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 183-197, April.
    3. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    4. Cotter, Kevin D., 1991. "Similarity of games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 501-520.
    5. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 409-434.
    6. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808, Elsevier.
    7. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    8. 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.
    9. Beth Allen, 1986. "The Demand for (Differentiated) Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 311-323.
    10. Van Zandt, Timothy, 2002. "Information, measurability, and continuous behavior," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 293-309, November.
    11. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2005. "On the continuity of equilibrium and core correspondences in economies with differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 793-812, November.
    12. João Correia-da-Silva & Carlos Hervés-Beloso, 2007. "Private Information: Similarity as Compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 395-407, March.
    13. 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.
    14. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    15. Halpern, Joseph Y., 2002. "Characterizing the Common Prior Assumption," Journal of Economic Theory, Elsevier, vol. 106(2), pages 316-355, October.
    16. 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.
    17. Dov Monderer & Dov Samet, 1996. "Proximity of Information in Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 707-725, August.
    18. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
    19. Cotter, Kevin D., 1987. "Convergence of information, random variables and noise," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 39-51, February.
    20. Allen, Beth, 1983. "Neighboring information and distributions of agents' characteristics under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 63-101, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. Khan, M. Ali & Yu, Haomiao & Zhang, Zhixiang, 2024. "On comparisons of information structures with infinite states," Journal of Economic Theory, Elsevier, vol. 218(C).
    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.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fukuda, Satoshi, 2019. "Epistemic foundations for set-algebraic representations of knowledge," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 73-82.
    2. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2005. "On the continuity of equilibrium and core correspondences in economies with differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 793-812, November.
    3. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2008. "Uniform Continuity of the Value of Zero-Sum Games with Differential Information," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 552-560, August.
    4. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    5. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    6. Barbie, Martin & Gupta, Abhishek, 2014. "The topology of information on the space of probability measures over Polish spaces," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 98-111.
    7. Ulrich Schwalbe, 1999. "The core of an exchange economy with asymmetric information," Journal of Economics, Springer, vol. 70(2), pages 155-185, June.
    8. Timothy Van Zandt & Kaifu Zhang, 2011. "A theorem of the maximin and applications to Bayesian zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 289-308, May.
    9. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    10. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    11. Klaus Nehring, 2003. "Common Priors For Like-Minded Agents," Economics Working Papers 0035, Institute for Advanced Study, School of Social Science.
    12. João Correia-da-Silva & Carlos Hervés-Beloso, 2007. "Private Information: Similarity as Compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 395-407, March.
    13. repec:ebl:ecbull:v:4:y:2003:i:11:p:1-12 is not listed on IDEAS
    14. Van Zandt, Timothy, 2002. "Information, measurability, and continuous behavior," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 293-309, November.
    15. Lipman, Barton L., 2010. "Finite order implications of common priors in infinite models," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 56-70, January.
    16. Robin Hanson, 2003. "For Bayesian Wannabes, Are Disagreements Not About Information?," Theory and Decision, Springer, vol. 54(2), pages 105-123, March.
    17. Marco Scarsini & Yossi Feinberg, 2003. "Rate of Arbitrage and Reconciled Beliefs," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-12.
    18. Halpern, Joseph Y., 2002. "Characterizing the Common Prior Assumption," Journal of Economic Theory, Elsevier, vol. 106(2), pages 316-355, October.
    19. Ezra Einy & Diego Moreno & Aner Sela, 2020. "Continuity and robustness of Bayesian equilibria in Tullock contests," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 333-345, October.
    20. Satoshi Fukuda, 2024. "On the consistency among prior, posteriors, and information sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 521-565, September.
    21. Felipe Zurita, 2001. "Speculation in Financial Markets: A Survey," Documentos de Trabajo 197, Instituto de Economia. Pontificia Universidad Católica de Chile..

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:44:y:2008:i:9-10:p:1024-1039. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.