Menu Auctions Under Asymmetric Information

We study menu auction games in which several principals influence the choice of a privately-informed agent by simultaneously offering action-contingent payments; the agent is free to accept any subset of the offers. Building on tools from non-smooth optimal control with type-dependent participation constraints, we provide necessary conditions for any equilibrium allocation as the (constrained) maximizer of an endogenous aggregate virtual-surplus program. The aggregate maximand includes an information-rent component which captures how the principals’ rent-extraction motives combine. Although there is a large set of equilibria, including equilibrium allocations with discontinuities, we isolate one particular equilibrium allocation, the maximal allocation, which is the solution to an unconstrained maximization program. Under weak conditions, necessary conditions for a maximal allocation are also sufficient, and the corresponding equilibrium tariff offers are easily constructed. We illustrate our findings and derive some economic implications in several applications, with principals having either congruent interests (e.g., public goods collective action games), opposed interests (e.g., pork barrel politics, lobbying), and protection for sale in an international trade context.