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A partial folk theorem for games with private learning


  • Thomas Wiseman

    1. Department of Economics, University of Texas at Austin; wiseman@austin.utexas.edu
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    • I thank participants at the 2008 Workshop on Recent Advances in Repeated Games at the Stony Brook Game Theory Festival (especially Johannes Hörner, George Mailath, David Miller, Larry Samuelson, and Tristan Tomala) and the 2008 Conference on Strategic Information Acquisition and Transmission, funded by SFB TR 15, as well as seminar audiences and two anonymous referees, for helpful comments. This material is based on work supported by the National Science Foundation under Grant SES-0614654.


The payoff matrix of a finite stage game is realized randomly and then the stage game is repeated infinitely. The distribution over states of the world (a state corresponds to a payoff matrix) is commonly known, but players do not observe nature's choice. Over time, they can learn the state in two ways. After each round, each player observes his own realized payoff (which may be stochastic, conditional on the state) and he observes a noisy public signal of the state (whose informativeness may vary with the actions chosen). Actions are perfectly observable. The result is that for any function that maps each state to a payoff vector that is feasible and individually rational in that state, there is a sequential equilibrium in which patient players learn the realized state with arbitrary precision and achieve a payoff close to the one specified for that state. That result extends to the case where there is no public signal, but instead players receive very closely correlated private signals of the vector of realized payoffs.