Sequential screening with unknown mean and spread

We study a sequential screening problem in which the information structure is characterized by neither first-order stochastic dominance (FOSD) nor mean-preserving spread (MPS). Specifically, we refer to a procurement contract for an activity entailing a cost of γ = θ + εσ. There is private information on the mean θ and the spread σ, prior to contracting; and private observation of the zero-mean shock ε, after contracting. As in the literature on sequential screening, the screening instrument is the probability of the transaction taking place. At optimum, types are divided into groups, and the same allocation is assigned to all types within a group, as a way to discourage both overstatement of the mean and understatement of the spread within that same group. The distortion induced in the allocation depends on within-group average efficiency and cost of information. Relative to a scenario with FOSD, all types are recommended execution of the project more often. Relative to a scenario with MPS, performance is recommended more often from low-spread types and less often from high-spread types.