Communication with tokens in repeated games on networks

A key obstacle to coordination and cooperation in many networked environments is that behavior in each bilateral relationship is not observable to individuals outside that relationship: that is, information is local. This paper investigates when players can use communication to replicate any outcome that would have been sustainable were this information public. A benchmark result is that if only cheap talk communication is possible then public information can only be replicated if the network is 2-connected: that is, if no player can prevent the flow of information to another. In contrast, the main result is that public information can always be replicated if in addition to cheap talk the players have access to undifferentiated tokens that can be freely transferred among neighbors (which bear some resemblance to certain models of fiat money). Sufficient conditions are provided for such tokens to expand the equilibrium payoff set, relative to what would be achievable without explicit communication or with cheap talk communication only.