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Beliefs in Repeated Games

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  • John H. Nachbar

Abstract

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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File URL: http://www.iser.osaka-u.ac.jp/library/dp/2003/DP0597.pdf
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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. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-40, September.
  2. Matthew Jackson & Ehud Kalai, 1995. "Social Learning in Recurring Games," Discussion Papers 1138, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
  4. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
  5. 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.
  6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  7. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
  8. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  9. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  10. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  11. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer, vol. 18(2), pages 303-326.
  12. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer, vol. 11(3), pages 643-655.
  13. Ehud Lehrer & Sylvain Sorin, 1998. "-Consistent equilibrium in repeated games," International Journal of Game Theory, Springer, vol. 27(2), pages 231-244.
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Cited by:
  1. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
  2. Sami Al-Suwailem, 2012. "Complexity and Endogenous Instability," ASSRU Discussion Papers 1203, ASSRU - Algorithmic Social Science Research Unit.
  3. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.

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