A Partial Folk Theorem for Games with Private Learning
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.
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- Gossner, Olivier & Vieille, Nicolas, 2003.
"Strategic learning in games with symmetric information,"
Games and Economic Behavior,
Elsevier, vol. 42(1), pages 25-47, January.
- GOSSNER, Olivier & VIEILLE, Nicolas, 1998. "Strategic learning in games with symmetric information," CORE Discussion Papers 1998023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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"A two Sided Reputation Result with Long Run Players,"
1510, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Atakan, Alp E. & Ekmekci, Mehmet, 2013. "A two-sided reputation result with long-run players," Journal of Economic Theory, Elsevier, vol. 148(1), pages 376-392.
- Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, June.
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