The folk theorem for irreducible stochastic games with imperfect public monitoring

Stochastic games with hidden states

“…This is a great simplification, but still the model is not as tractable as one would like: Since there are infinitely many possible posterior beliefs, we need to consider a stochastic game with infinite states. This is in a sharp contrast to past work that assumes finite states (Dutta (), Fudenberg and Yamamoto (), and Hörner et al ())…”

“…Dutta () characterizes the feasible and individually rational payoffs for patient players, and proves the folk theorem for the case of observable actions. Fudenberg and Yamamoto () and Hörner et al () extend his result to games with public monitoring. All these papers assume that the state of the world is publicly observable at the beginning of each period…”

“…In general, the analysis of stochastic games is different from that of repeated games, because the action today influences the distribution of the future states, which in turn influences the stage‐game payoffs in the future. To avoid this complication, various papers in the literature (e.g., Dutta (), Fudenberg and Yamamoto (), Hörner et al ()) consider a model that satisfies the payoff invariance condition, in the sense that when players are patient, the feasible and individually rational payoff set is invariant to the initial state. In such a model, even if someone deviates today and influences the distribution of the state tomorrow, it does not change the feasible payoff set in the continuation game from tomorrow, so continuation payoff can be chosen in a flexible way, just as in the standard repeated game.…”

Recursive Methods in Discounted Stochastic Games: An Algorithm forδ→ 1 and a Folk Theorem

“…Note that Assumptions F1 and F2 are weaker than the rank assumptions of Fudenberg and Yamamoto (2010). Note that Assumptions F1 and F2 are weaker than the rank assumptions of Fudenberg and Yamamoto (2010).…”

“…Unlike ours, Dutta's ingenious proof is constructive, extending ideas developed by Fudenberg and Maskin (1986) for the case of repeated games with perfect monitoring. In independent and simultaneous work, Fudenberg and Yamamoto (2010) provided a different, direct proof of the folk theorem for stochastic games with imperfect public monitoring under irreducibility, without a general characterization of the equilibrium payoff set. In independent and simultaneous work, Fudenberg and Yamamoto (2010) provided a different, direct proof of the folk theorem for stochastic games with imperfect public monitoring under irreducibility, without a general characterization of the equilibrium payoff set.…”