Numerical Solutions to Principal-Agent Problems

Abstract

A principal-agent problem is a mathematical framework for modelling contractual relationships, where a principal delegates tasks to an agent in exchange for reward. Many real life contracts are of this type. The agent does not have the same objectives as the principal and he possesses hidden information. Two types of hidden information is generally considered: moral hazard (hidden action) and adverse selection (hidden type). This asymmetry of information can be exploited by the agent for his own benefits, which can reduce the principal's utility. The goal is find a mechanism, in the form of a contract, that aligns the principal's and agent's objectives and maximises the principal's utility. Previous economic studies focuses on finding analytical solutions on specific cases. In this study we consider numerical solution approaches for a principal agent-problem with moral hazard, and a generalised principal-agent problem with moral hazard and adverse selection problem. The moral hazard problem is a bi-level programming problem and it is solved by assuming the agent's optimal effort is an implicit function dependent on the contract. The generalised principal agent problem is an infinite programming problem. For that we propose two numerical solution methods: the discretisation method and the basis function method. Both are tested on a option contract problem with moral hazard and adverse selection. From the experiment, the discretisation method seems to be the better performer.