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Beliefs in Repeated Games

  • John H. Nachbar

Consider a two-player discounted infinitely repeated game. A player's belief is a probability distribution over the opponent's repeated game strategies. This paper shows that, for a large class of repeated games, there are no beliefs that satisfy three conditions, learnability, consistency, and a diversity condition, CS. This impossibility theorem generalizes results in Nachbar (1997).

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Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0597.

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Date of creation: Sep 2003
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Handle: RePEc:dpr:wpaper:0597
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  1. Ehud Kalai & Ehud Lehrer, 1991. "Subjective Equilibrium in Repeated Games," Discussion Papers 981, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer, vol. 11(3), pages 643-655.
  3. Jackson, Matthew O. & Kalai, Ehud, 1997. "Social Learning in Recurring Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 102-134, October.
  4. Ehud Lehrer & Sylvain Sorin, 1998. "-Consistent equilibrium in repeated games," International Journal of Game Theory, Springer, vol. 27(2), pages 231-244.
  5. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer, vol. 18(2), pages 303-326.
  6. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
  7. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
  8. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
  9. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  10. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1998. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Discussion Papers 1228, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  12. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  13. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
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