Abstract
In the context of learning in games, belief learning refers to models in which players are engaged in a dynamic game and each player optimizes with respect to a prediction rule that gives a forecast of next-period opponent behaviour as a function of the current history. This article focuses on the most studied class of dynamic games, namely, two-player discounted repeated games with finite stage game action sets and perfect monitoring.
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Bibliography
Aoyagi, M. 1996. Evolution of beliefs and the Nash equilibrium of normal form games. Journal of Economic Theory 70: 444–469.
Bernheim, B.D. 1984. Rationalizable strategic behavior. Econometrica 52: 1007–1028.
Brown, G.W. 1951. Iterative solutions of games by fictitious play. In Activity analysis of production and allocation, ed. T.J. Koopmans. New York: Wiley.
Cournot, A. 1838. Researches into the Mathematical Principles of the Theory of Wealth. Trans. N.T. Bacon, New York: Kelley, 1960.
Dawid, A.P. 1985. The impossibility of inductive inference. Journal of the American Statistical Association 80: 340–341.
Foster, D., and P. Young. 2001. On the impossibility of predicting the behavior of rational agents. Proceedings of the National Academy of Sciences 98: 12848–12853.
Foster, D., and P. Young. 2003. Learning, hypothesis testing, and Nash equilibrium. Games and Economic Behavior 45: 73–96.
Fudenberg, D., and D. Kreps. 1993. Learning mixed equilibria. Games and Economic Behavior 5: 320–367.
Fudenberg, D., and D. Levine. 1993. Steady state learning and Nash equilibrium. Econometrica 61: 547–574.
Fudenberg, D., and D. Levine. 1995. Universal consistency and cautious fictitious play. Journal of Economic Dynamics and Control 19: 1065–1089.
Fudenberg, D., and D. Levine. 1998. Theory of learning in games. Cambridge, MA: MIT Press.
Fudenberg, D., and D. Levine. 1999. Conditional universal consistency. Games and Economic Behavior 29: 104–130.
Harsanyi, J. 1973. Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points. International Journal of Game Theory 2: 1–23.
Hart, S., and A. Mas-Colell. 2003. Uncoupled dynamics do not lead to Nash equilibrium. American Economic Review 93: 1830–1836.
Hart, S., and A. Mas-Colell. 2006. Stochastic uncoupled dynamics and Nash equilibrium. Games and Economic Behavior 57: 286–303.
Hofbauer, J., and W. Sandholm. 2002. On the global convergence of stochastic fictitious play. Econometrica 70: 2265–2294.
Jackson, M., and E. Kalai. 1999. False reputation in a society of players. Journal of Economic Theory 88: 40–59.
Jordan, J.S. 1991. Bayesian learning in normal form games. Games and Economic Behavior 3: 60–81.
Jordan, J.S. 1993. Three problems in learning mixed-strategy Nash equilibria. Games and Economic Behavior 5: 368–386.
Jordan, J.S. 1995. Bayesian learning in repeated games. Games and Economic Behavior 9: 8–20.
Kalai, E., and E. Lehrer. 1993a. Rational learning leads to Nash equilibrium. Econometrica 61: 1019–1045.
Kalai, E., and E. Lehrer. 1993b. Subjective equilibrium in repeated games. Econometrica 61: 1231–1240.
Kuhn, H.W. 1964. Extensive games and the problem of information. In Contributions to the theory of games, ed. M. Dresher, L.S. Shapley, and A.W. Tucker, Vol. 2. Princeton: Princeton University Press.
Milgrom, P., and J. Roberts. 1991. Adaptive and sophisticated learning in repeated normal form games. Games and Economic Behavior 3: 82–100.
Milgrom, P., and R. Weber. 1985. Distributional strategies for games with incomplete information. Mathematics of Operations Research 10: 619–632.
Nachbar, J.H. 2001. Bayesian learning in repeated games of incomplete information. Social Choice and Welfare 18: 303–326.
Nachbar, J.H. 2005. Beliefs in repeated games. Econometrica 73: 459–480.
Noguchi, Y. 2005. Merging with a set of probability measures: A characterization. Working paper, Kanto Gakuin University.
Nyarko, Y. 1998. Bayesian learning and convergence to Nash equilibria without common priors. Economic Theory 11: 643–655.
Oakes, D. 1985. Self-calibrating priors do not exist. Journal of the American Statistical Association 80: 339–342.
Sandroni, A. 1998. Necessary and sufficient conditions for convergence to Nash equilibrium: the almost absolute continuity hypothesis. Games and Economic Behavior 22: 121–147.
Sandroni, A. 2000. Reciprocity and cooperation in repeated coordination games: The principled-player approach. Games and Economic Behavior 32: 157–182.
Shapley, L. 1962. On the nonconvergence of fictitious play. Discussion Paper RM-3026, RAND.
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Nachbar, J. (2018). Learning and Evolution in Games: Belief Learning. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2645
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2645
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