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Finite Order Implications of Common Priors

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  • Barton L. Lipman

Abstract

I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that in finite models, the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any finite N and any finite partitions model where priors have the same support, there is another finite partitions model with common priors that has the same nth order beliefs and knowledge for all n≤N. Copyright The Econometric Society 2003.

Suggested Citation

  • Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, vol. 71(4), pages 1255-1267, July.
  • Handle: RePEc:ecm:emetrp:v:71:y:2003:i:4:p:1255-1267
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    References listed on IDEAS

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    1. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
    2. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    5. Nyarko, Yaw, 1991. "Most Games Violate the Harsanyi Doctrine," Working Papers 91-39, C.V. Starr Center for Applied Economics, New York University.
    6. Werlang, Sérgio Ribeiro da Costa, 1988. "Common knowledge," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 118, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
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    Citations

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    Cited by:

    1. Kim-Sau Chung & J.C. Ely, 2007. "Foundations of Dominant-Strategy Mechanisms," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 447-476.
    2. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    3. Oyama, Daisuke & Tercieux, Olivier, 2010. "Robust equilibria under non-common priors," Journal of Economic Theory, Elsevier, vol. 145(2), pages 752-784, March.
    4. Oyama, Daisuke & Tercieux, Olivier, 2012. "On the strategic impact of an event under non-common priors," Games and Economic Behavior, Elsevier, vol. 74(1), pages 321-331.
    5. 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.
    6. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on types," Theoretical Economics, Econometric Society, vol. 1(3), pages 275-309, September.
    7. repec:eee:mateco:v:75:y:2018:i:c:p:13-18 is not listed on IDEAS
    8. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    9. Angeletos, George-Marios & La’O, Jennifer, 2009. "Incomplete information, higher-order beliefs and price inertia," Journal of Monetary Economics, Elsevier, vol. 56(S), pages 19-37.
    10. Tsakas Elias, 2012. "Rational belief hierarchies," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    12. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
    13. Takashi Kunimoto, 2006. "The Robustness Of Equilibrium Analysis: The Case Of Undominated Nash Equilibrium," Departmental Working Papers 2006-26, McGill University, Department of Economics.
    14. Barelli, Paulo, 2009. "Consistency of beliefs and epistemic conditions for Nash and correlated equilibria," Games and Economic Behavior, Elsevier, vol. 67(2), pages 363-375, November.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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