Optimal Contracts for Agents with Adverse Selection

Chao Li,Zhijian Qiu

doi:10.1155/2020/9317019

Abstract

Due to information asymmetry, adverse selection exists largely in the multiagent market. Aiming at these problems, we develop two models: pure adverse selection model and mixed adverse selection and moral hazard model. We make the assumption that a type of agent is discrete and effort level is continuous in the models. With these models, we investigate the characters that make an optimal contract as well as the conditions under which the utility of a principal and agents can be optimized. As a result, we show that, in the pure adverse selection model, the conditions to reach the optimal utility of a principal and individual agents are that a principal needs to design different contracts for different types of agents, and an individual agent chooses the corresponding type of contracts. For the mixed model, we show that incentive constraint for agents plays a very important role. In fact, we find that whether a principal provides high-type contract or a separating equilibrium contract depends on the probability of existence of low-type agents in the market. In general, if a separating equilibrium contract is issued, then information asymmetry will cause the utility of the high-type agents to be less than that of the case in full information.

Highlights

In modern economy and financial market, information asymmetry can cause adverse selection problems between a principal and agents. is means that a principal is not able to know which type of an agent is before a contract is signed to represent the type of agents. e agents with high production costs are defined low-type (L-type) agents, and the agents with low production costs are defined as high-type (H-type) agents
By investigating the old car market, he concluded that information asymmetry between buyers and sellers may lead to adverse selection problems
We develop a continuous-time model for modeling a multiagent relationship in the presence of adverse selection, with or without moral hazard

Summary

Introduction

In modern economy and financial market, information asymmetry can cause adverse selection problems between a principal and agents. is means that a principal is not able to know which type of an agent is before (or after) a contract is signed (in this paper, we use the level of production costs or the level of investment income) to represent the type of agents. e agents with high production costs are defined low-type (L-type) agents, and the agents with low production costs are defined as high-type (H-type) agents. Sung [10] adds the adverse selection problem to the pure moral hazard model (the most famous continuous-time principal-agent model, see [11,12,13]) in a continuous time and studies a mixed model of risk aversion agent controlling drift and volatility. In the pure adverse selection model, due to information asymmetry, a principal has the motivation to provide “menu contracts” to ensure that each agent of a certain type accepts a contract designed for his/her type, rather than choosing types of other agents.

The Model

Second Best

Third Best

Conclusion