Optimal auction design and irrelevance of private information

We consider the problem of mechanism design by a principal who has private information. We point out a simple condition under which the privacy of the principal's information is irrelevant in the sense that the mechanism implemented by the principal coincides with the mechanism that would be optimal if the principal's information were publicly known. This condition is then used to show that the privacy of the principal's information is irrelevant in many environments with private values and quasi-linear preferences, including the Myerson's classical auction environments in which the seller is privately informed about her cost of selling. Our approach unifies results by Maskin and Tirole, Tan, Yilankaya, Skreta, and Balestrieri. We also provide an example of a classical principal-agent environment with private values and quasi-linear preferences where a privately informed principal can do better than when her information is public.