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How to make sense of the common prior assumption under incomplete information

Author

Listed:
  • Giacomo Bonanno

    () (Department of Economics, University of California, Davis, CA 95616-8578, USA)

  • Klaus Nehring

    () (Department of Economics, University of California, Davis, CA 95616-8578, USA)

Abstract

Recent contributions have questioned the meaningfulness of the Common Prior Assumption (CPA) in situations of incomplete information. We characterize the CPA in terms of the primitives (individuals' belief hierarchies) without reference to an ex ante stage. The key is to rule out "agreeing to disagree" about any aspect of beliefs. Our results also yield a generalization of single-person Bayesian updating to situations without perfect recall. The entire analysis is carried out locally at the "true state", using beliefs only, rather than beliefs-plus-knowledge. We discuss the role of truth assumptions on beliefs for a satisfactory notion of the CPA, and point out an important conceptual discontinuity between the case of two and many individuals.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:28:y:1999:i:3:p:409-434
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    Citations

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    Cited by:

    1. Robin Hanson, 2003. "For Bayesian Wannabes, Are Disagreements Not About Information?," Theory and Decision, Springer, vol. 54(2), pages 105-123, March.
    2. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    3. Chen, Yi-Chun & Lehrer, Ehud & Li, Jiangtao & Samet, Dov & Shmaya, Eran, 2015. "Agreeing to agree and Dutch books," Games and Economic Behavior, Elsevier, vol. 93(C), pages 108-116.
    4. Marco Scarsini & Yossi Feinberg, 2003. "Rate of Arbitrage and Reconciled Beliefs," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-12.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    6. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    7. 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.
    8. repec:wsi:igtrxx:v:08:y:2006:i:01:n:s0219198906000795 is not listed on IDEAS
    9. Hellman, Ziv, 2011. "Iterated expectations, compact spaces, and common priors," Games and Economic Behavior, Elsevier, vol. 72(1), pages 163-171, May.
    10. repec:ebl:ecbull:v:4:y:2003:i:11:p:1-12 is not listed on IDEAS
    11. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    12. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 399-410, May.
    13. Ziv Hellman, 2012. "Deludedly Agreeing to Agree," Discussion Paper Series dp605, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    14. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    15. Ming Pu & Gang-Zhi Fan & Yongheng Deng, 2014. "Breakeven Determination of Loan Limits for Reverse Mortgages under Information Asymmetry," The Journal of Real Estate Finance and Economics, Springer, vol. 48(3), pages 492-521, April.
    16. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, vol. 119(2), pages 247-270, December.
    17. Halpern, Joseph Y., 2002. "Characterizing the Common Prior Assumption," Journal of Economic Theory, Elsevier, vol. 106(2), pages 316-355, October.
    18. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
    19. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    20. Pierpaolo Battigalli, 2006. "Rationalization In Signaling Games: Theory And Applications," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 67-93.
    21. Klaus Nehring, 2003. "Common Priors For Like-Minded Agents," Economics Working Papers 0035, Institute for Advanced Study, School of Social Science.
    22. 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.
    23. Giacomo Bonanno, 2009. "A characterization of sequential equilibrium in terms of AGM belief revision," Working Papers 914, University of California, Davis, Department of Economics.
    24. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

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