Screening for Choice Sets

TL;DR

This paper addresses screening where private information concerns feasible technology sets rather than payoff parameters, and agents can conceal available technologies to affect the principal's option set. By imposing a nested inclusion order on technology sets, the authors decompose the principal’s design problem into choosing a monotone promised utility $U(T)$ and then selecting a payoff within the induced feasible set to satisfy that promise; the optimal mechanism exhibits a bang-bang structure, with at most $K$ flat segments where $K$ is the number of downward-sloping segments of the complete-information curve $u_c(T)$. The complete-information benchmark curve $u_c(T)$ guides when the principal fully exploits new feasibility versus when she compresses rewards to sustain truthful disclosure, and the number of flat regions is bounded by $K$, enabling a dynamic-programming computation. The results yield practical implications for institutional design, explaining why richer feasibility can coincide with flat promised utilities and why reward compression may accompany under-use of newly disclosed options. The framework applies to manage persuasion, action elicitation, and production-technology contracts, offering sharp, testable predictions about when and how disclosures are rewarded or constrained in organizations and regulation.

Abstract

We study a screening problem in which an agent privately observes a set of feasible technologies and can strategically disclose only a subset to the principal. The principal then takes an action whose payoff consequences for both players are publicly known. Under the assumption that the possible technology sets are ordered by set inclusion, we show that the optimal mechanism promises the agent a utility that is weakly increasing as the reported set expands, and the choice of the principal maximizes her own utility subject to this promised utility constraint. Moreover, the optimal promised utility either coincides with the agent's utility under the complete information benchmark or remains locally constant, with the number of constant segments bounded by the number of downward-sloping segments of the complete information benchmark.

Figures (2)

• Figure 1: Illustration of monotone closures and optimal promised utility.
• Figure 2: Illustration for Lemma 4: a monotone promised utility $U(T)$ that lies outside the monotone envelope can be projected into the envelope by clamping to $\bar{u}_c(T)$ where it violates feasibility/optimality; this projection weakly increases the principal's payoff.

Theorems & Definitions (28)

• Proposition 1
• Corollary 1
• Lemma 1
• Lemma 2
• Lemma 3
• Lemma 4
• Theorem 1: Optimal Mechanisms
• Proposition 2
• Proposition 3
• Definition 1: Technology expansion dominance