Principal-agent problems with adverse selection: A stochastic target problem formulation

2026-05-01

AI Summary

This study addresses the adverse selection problem in principal-agent settings under information asymmetry when the principal is restricted to offering a single contract. By reformulating the agent’s optimization problem as a stochastic target problem, the authors characterize the agent’s credible set and cast the principal’s problem as a stochastic optimal control problem with partial information and state constraints. This work is the first to integrate the single-contract adverse selection framework with the stochastic target approach, thereby uncovering the source of value in screening contracts. The proposed method successfully solves the principal’s optimization problem and quantifies the welfare loss incurred by conventional screening mechanisms under the single-contract restriction, highlighting the model’s theoretical and practical relevance for mechanism design.

Abstract

We study a principal-agent problem with adverse selection, where the principal does not know the agent's true cost but must design a contract to optimize a specific criterion. Unlike standard screening frameworks that allow for self-selection, we assume the principal can only offer a unique contract. We show that the agent's optimization problem can be reformulated as a stochastic target problem. After characterizing the credible domain of this target problem, we show that the principal's objective can be solved as a stochastic optimal control problem with partial information and state constraints. The description of the credible domain also allows us to obtain the value of screening contracts.

Problem

• principal-agent problem
• adverse selection
• contract design
• stochastic target problem
• screening

Innovation

• stochastic target problem
• principal-agent problem
• adverse selection
• partial information
• state constraints