Online Concealed Correlation and Bounded Rationality

Correlation of players' actions may evolve in the common course of the play of a repeated game with perfect monitoring (``obline 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 obline correlation of the actions of ``weak'' players, where this correlation is concealed from an opponent of ``intermediate'' strength. The feasibility of such ``\ol 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, each of which captures a different aspect of bounded rationality. In the first, players use bounded recall strategies. In the second, players use strategies that are implementable by finite automata.