Sequential screening and the relationship between principal's preferences and agent's incentives

In sequential screening problems it is found that, under some regularity conditions, local incentive compatibility constraints are sufficient for implementability. However, this follows from the assumption that the possible distributions of the unknown variable satisfy either first-order stochastic dominance or mean-preserving spread. That assumption is matched with private information about either the expected value or the spread of the variable. In this paper we allow for private information about both parameters. In a setting with four possible cost distributions, two with equal expected values and different spreads and two with different expected values and equal spreads, we show that there can be multiple combinations of binding incentive constraints depending on the principal's preferences. The less concave / more convex that the marginal surplus is, the more that the binding incentive constraints are related to private information about one parameter of the distribution relative to the other. Yet, screening is always two-dimensional. Local incentive constraints are sufficient, as in the literature, only when the marginal surplus is sufficiently convex. We further suggest that, in the same vein as in Consumption theory, the contractual choice can be regarded as mirroring the preference of the decision-maker for a lottery that occasions a higher (certain) cost but grants the possibility of facing more efficient (random) outcomes. Resting on this interpretation, we assess that the benefit of screening the agent in two stages, rather than in the contracting stage only, is higher when the marginal surplus is less concave / more convex.