Informed Principal In Quasi-Linear Environments

This paper studies the problem of mechanism selection by an informed principal in general quasi-linear environments. Our model allows for large and continuous type spaces, multiple agents, and interdependent preferences. We provide conditions that guarantee that an essentially unique Perfect Bayesian equilibrium exists, coincides with Myerson’s strong solution and with the ex-ante optimal allocation, and consists of allocations that would be optimal if the principal’s information were publicly known. We demonstrate that these conditions are satisfied in a broad range of settings, including Myerson’s optimal auction setting. Finally, we present three examples of quasi-linear environments with independent private values where our conditions fail and Myerson’s strong solution does not exist. In the first example, some type of the principal will use bunching if her type is publicly known, but the resulting allocation rule is dominated by one in which the principal does not use bunching if her type is private information. This example is important because it demonstrates that the seminal results of Maskin and Tirole’s [12] for quasi-linear environments do not immediately extend to environments with more than two types of the agent. In the second example, there is a chance that the seller knows the buyer’s valuation. In the third example, the seller has uncertain supply of the good.