Online concealed correlation and bounded rationality

- We consider repeated games with players whose complexity is bounded.
- A group of “weak” players wish to correlate their actions.
- “Strong” players guide them by their public actions.
- The correlation is concealed from an “intermediate” opponent.
- We derive a folk theorem for a class of repeated games with bounded complexity.

Correlation of players' actions may evolve in the common course of the play of a repeated game with perfect monitoring (“online correlation”). In this paper we study the concealment of such correlation from a boundedly rational player. We show that “strong” players, i.e., players whose strategic complexity is less stringently bounded, can orchestrate the online correlation of the actions of “weak” players, where this correlation is concealed from an opponent of “intermediate” strength. The feasibility of such “online concealed correlation” is reflected in the individually rational payoff of the opponent and in the equilibrium payoffs of the repeated game.This result enables the derivation of a folk theorem that characterizes the set of equilibrium payoffs in a class of repeated games with boundedly rational players and a mechanism designer who sends public signals.The result is illustrated in two models, bounded recall strategies and finite automata.