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Approximate Common Knowledge Revisited


  • Stephen Morris


Suppose, we replace "knowledge" by "belief with probability p" in standard definitions of common knowledge. Very different notions arise depending on the exact definition of common knowledge used in the substitution. This paper demonstrates those diffrences and identifies which notion is relevant in each of three contexts: equilibrium analysis in incomplete information games, best response dynamics in incomplete information games, and agreeing to disagree/no trade results.
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Suggested Citation

  • Stephen Morris, "undated". "Approximate Common Knowledge Revisited," Penn CARESS Working Papers 6be11f49fbded40b2a623aebf, Penn Economics Department.
  • Handle: RePEc:cla:penntw:6be11f49fbded40b2a623aebfa5361c6

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    References listed on IDEAS

    1. Hyun Song Shin, 1996. "Comparing the Robustness of Trading Systems to Higher-Order Uncertainty," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 39-59.
    2. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    3. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-157, January.
    4. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, July.
    5. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    6. Lismont L. & Mongin, P., 1996. "Belief closure: A semantics of common knowledge for modal propositional logic," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 60-60, February.
    7. Shin Hyun Song, 1993. "Logical Structure of Common Knowledge," Journal of Economic Theory, Elsevier, vol. 60(1), pages 1-13, June.
    8. Shin, Hyun Song & Williamson, Timothy, 1996. "How Much Common Belief Is Necessary for a Convention?," Games and Economic Behavior, Elsevier, vol. 13(2), pages 252-268, April.
    9. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    10. 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).
    11. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    12. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
    13. Stephen Morris, "undated". "Co-operation and Timing," Penn CARESS Working Papers b8d506ba7aa15345b602bb4eb, Penn Economics Department.
    14. Geanakoplos, John, 1994. "Common knowledge," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 40, pages 1437-1496 Elsevier.
    15. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, July.
    16. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
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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. Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2008. "Common Learning," Econometrica, Econometric Society, vol. 76(4), pages 909-933, July.
    3. Martin Cripps & Jeffrey Ely & George Mailath & Larry Samuelson, 2013. "Common learning with intertemporal dependence," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 55-98, February.
    4. Christian Schmidt, 2006. "Quelques points de rencontre entre économistes et psychologues," Revue économique, Presses de Sciences-Po, vol. 57(2), pages 242-257.
    5. Cy Maor & Eilon Solan, 2015. "Cooperation under incomplete information on the discount factors," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 321-346, May.
    6. Wilson Perez, 2004. "Divide and Conquer: Noisy Communication in Networks, Power, and Wealth Distribution," Working Papers 2004.33, Fondazione Eni Enrico Mattei.
    7. Romeo Matthew Balanquit, 2016. "Common Belief Revisited," UP School of Economics Discussion Papers 201608, University of the Philippines School of Economics.
    8. Stephen Morris & Hyun Song Shin, 2012. "Contagious Adverse Selection," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(1), pages 1-21, January.

    More about this item

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations


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