Common agency with informed principals: Menus and signals

This paper considers general games in which multiple informed principals simultaneously compete to influence the decisions of a common agent. It shows that we can characterize all outcomes of any game in which principals delegate the final decisions to the agent using arbitrary mechanisms, by studying a simpler game in which they can offer only menus of decisions and send cheap-talk signals to the agent. For games in which the principals instead participate in making final decisions, we can characterize all their outcomes by studying a simpler game in which principals can again send cheap-talk signals but can offer only menus of direct mechanisms, to which they report their information truthfully.