Online Concealed Correlation by Boundedly Rational Players

In a repeated game with perfect monitoring, correlation among a group of players may evolve in the common course of play (online correlation). Such a correlation may be concealed from a boundedly rational player. The feasibility of such “online concealed correlation” is quantified by the individually rational payoff of the boundedly rational player. We show that “strong” players, i.e., players whose strategic complexity is less stringently bounded, can orchestrate online correlation of the actions of “weak” players, in a manner that is concealed from an opponent of “intermediate” strength. The result is illustrated in two models, each captures another aspect of bounded rationality. In the first, players use bounded recall strategies. In the second, players use strategies that are implementable by finite automata.

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