Menu Auctions and Influence Games with Private Information

Abstract

We study influence games in which n principals attempt to influence the choice of a privately-informed agent by offering payment menus (i.e., nonlinear transfer schedules) which promise monetary rewards in exchange for actions by the agent.We provide a simple necessary condition which characterizes the equilibrium set (both continuous and discontinuous) as the solution to a program which maximizes the principals’ “aggregate” virtual surplus over the set of the agent’s equilibrium choices. In every such program, the information-rent term is the same conflation of the individual principals’ objectives and there are two distinct sources of inefficiencies: inefficient contracting by a given coalition of active principals and inefficient activity by principals. One noteworthy subset of equilibrium allocations with several desirable properties is the maximal allocation. These allocations are straightforward to compute and are supported by continuously differentiable transfer functions. Our results are illustrated by means of two games: a public goods game in which each player simultaneously offers a menu contract to a common provider of the public good in order to induce greater supply, and a lobbying game between conflicting interest groups in which members from each group offer menus of contributions to a common political decision-maker in an attempt to influence policymaking. The nature of equilibrium distortions and the impact of changes in principal preferences (size of stake holders, etc.) on the equilibrium level of influence and extraction of information rents are explored.