Principal-agent problems with adverse selection: A stochastic target problem formulation
Guillermo Alonso Alvarez, Ibrahim Ekren, Liwei Huang
TLDR
This paper reformulates principal-agent problems with adverse selection and unique contracts into stochastic target and optimal control problems.
Key contributions
- Reformulates the agent's optimization problem as a stochastic target problem.
- Characterizes the credible domain of the reformulated stochastic target problem.
- Solves the principal's objective as a stochastic optimal control problem with partial information.
- Obtains the value of screening contracts using the description of the credible domain.
Why it matters
This work offers a novel approach to principal-agent problems under adverse selection, especially when only a unique contract can be offered. It provides a robust framework using stochastic control, which can help design more effective contracts in real-world scenarios.
Original 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.
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