Theoretical Economics, Volume 14, Number 3 (July 2019)

Theoretical Economics 14 (2019), 1115–1167

Stochastic games with hidden states

Yuichi Yamamoto


This paper studies infinite-horizon stochastic games in which players observe payoffs and noisy public information about a hidden state each period. We find that, very generally, the feasible and individually rational payoff set is invariant to the initial prior about the state in the limit as the discount factor goes to one. This result ensures that players can punish or reward the opponents via continuation payoffs in a flexible way. Then we prove the folk theorem, assuming that public randomization is available. The proof is constructive, and uses the idea of random blocks to design an effective punishment mechanism.

Keywords: Stochastic game, hidden state, uniform connectedness, robust connectedness, random blocks, folk theorem

JEL classification: C72, C73

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