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International Journal of Game Theory

, Volume 42, Issue 1, pp 55–98 | Cite as

Common learning with intertemporal dependence

  • Martin W. Cripps
  • Jeffrey C. Ely
  • George J. Mailath
  • Larry Samuelson
Article

Abstract

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. Will the agents commonly learn the value of the parameter, i.e., will the true value of the parameter become approximate common-knowledge? If the signals are independent and identically distributed across time (but not necessarily across agents), the answer is yes (Cripps et al., Econometrica, 76(4):909–933, 2008). This paper explores the implications of allowing the signals to be dependent over time. We present a counterexample showing that even extremely simple time dependence can preclude common learning, and present sufficient conditions for common learning.

Keywords

Common learning Common belief Private signals Private beliefs 

JEL Classification

D82 D83 

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References

  1. Billingsley P (1979) Probability and measure, 1st edn. Wiley, New YorkGoogle Scholar
  2. Brémaud P (1999) Markov chains: Gibbs fields, Monte Carlo simulation, and queues. Springer, New YorkGoogle Scholar
  3. Cesa-Bianchi N, Lugosi G (2006) Prediction, learning, and games. Cambridge University Press, New YorkCrossRefGoogle Scholar
  4. Cover TM, Thomas JA (1991) Elements of information theory. Wiley, New YorkCrossRefGoogle Scholar
  5. Cripps MW, Ely JC, Mailath GJ, Samuelson L (2008) Common learning. Econometrica 76(4): 909–933CrossRefGoogle Scholar
  6. den Hollander F (2000) Large deviations. American Mathematical Society, ProvidenceGoogle Scholar
  7. Ephraim Y, Merhav N (2002) Hidden Markov processes. IEEE Trans Inf Theory 48(6): 1518–1569CrossRefGoogle Scholar
  8. Halpern JY, Moses Y (1990) Knowledge and common knowledge in a distributed environment. J ACM 37: 549–587CrossRefGoogle Scholar
  9. Monderer D, Samet D (1989) Approximating common knowledge with common beliefs. Games Econ Behav 1(2): 170–190CrossRefGoogle Scholar
  10. Morris S (1999) Approximate common knowledge revisited. Int J Game Theory 28(3): 385–408CrossRefGoogle Scholar
  11. Rubinstein A (1989) The electronic mail game: Strategic behavior under almost common knowledge. Am Econ Rev 79(3): 385–391Google Scholar
  12. Steiner J, Stewart C (2011) Communication, timing, and common learning. J Econ Theory 146(1): 230–247CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Martin W. Cripps
    • 1
  • Jeffrey C. Ely
    • 2
  • George J. Mailath
    • 3
  • Larry Samuelson
    • 4
  1. 1.Department of EconomicsUniversity College LondonLondonUK
  2. 2.Department of EconomicsNorthwestern UniversityEvanstonUSA
  3. 3.Department of EconomicsUniversity of PennsylvaniaPhiladelphiaUSA
  4. 4.Department of EconomicsYale UniversityNew HavenUSA

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