Mechanism Design by an Informed Principal: The Quasi-Linear Private-Values Case

Abstract

We show that, in environments with independent private values and transferable utility, a privately informed principal can solve her mechanism selection problem by implementing an allocation that is ex-ante optimal for her. No type of the principal can gain from proposing an alternative mechanism that is incentivefeasible with any belief that puts probability 0 on types that would strictly lose from proposing the alternative. We show that the solution exists in essentially any environment with finite type spaces, and in any linear-utility environment with continuous type spaces, allowing for arbitrary disagreement outcomes. As an application, we consider a bilateral exchange environment (Myerson and Satterthwaite, 1983) in which the principal is one of the traders. If the property rights over the good are dispersed among the traders, then the principal will implement an allocation in which she is almost surely better off than if her type is commonly known. The optimal mechanism is a combination of a participation fee, a buyout option for the principal, and a resale stage with posted prices and, hence, is a generalization of the posted price that would optimal if the principal's valuation were commonly known.