joint with A. Vinella

We consider a two-dimensional and sequential screening problem in which the principal faces four possible distributions (types) in the contracting stage: two with equal expected values and different spreads and two with different expected values and equal spreads. These distributions can be ordered according to neither first-order stochastic dominance nor mean-preserving spread, leading to many possible combinations of binding incentive constraints. We show that those constraints that are relevant in contractual design are related, in the end, to the principal's preferences with respect to the good. This relationship is key to conveniently narrowing the set of incentive constraints to be considered in specific applications. The less concave / more convex that marginal surplus is with respect to quantity, the more that the principal is concerned with the possibility of the agent misrepresenting the spread rather than the expected value and vice versa, depending on whether the uncertainty about the expected value is greater than the uncertainty about the spread. We also show that the bunching of types might be optimal to limit distortions rather than removing conflicts between incentive constraints, as is most common in the literature. Finally, we characterize the optimal contract for one possible type ordering.
Keywords: Sequential screening; multidimensional screening; expected cost; spread; marginal surplus function

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