Menu Auctions and Influence Games with Private Information

We study games in which multiple principals influence the choice of a privately-informed agent by offering action-contingent payments. We characterize the equilibrium allocation set as the maximizers of an endogenous aggregate virtual-surplus program. The aggregate maximand for every equilibrium includes an information-rent margin which captures the confluence of the principals’ rent-extraction motives. We illustrate the economic implications of this novel margin in two applications: a public goods game in which players incentivize a common public good supplier, and a lobbying game between conflicting interest groups who offer contributions to influence a common political decision-maker.