We analyze optimal trading mechanisms in environments where each trader owns some units of a good to be traded and may be either a seller or a buyer, depending on the realization of privately observed valuations. First, the concept of virtual valuation is extended to ex ante unidentified...

In a general framework with independent private values of the bidders, we propose a game, with a simple economic interpretation, that allows implementing the optimal auction outcome when the seller ignores the distributions of the different bidders' valuations. In this robust or detail-free...

I consider the problem of the design of an optimal self-selecting contract scheme for a principal who is buying a good from an agent which has the opportunity of making a cost-reducing unobservable investment prior to the contracting stage. Because of a hold-up problem, the agent will randomize...