A Dynamic Principal Agent Problem with One-sided Commitment

TL;DR

This paper models a dynamic principal-agent problem allowing the agent to quit at a cost, revealing that flexible, non-committal contracts can be more optimal than traditional ones, with implications for hiring strategies and contract design.

Contribution

It characterizes the principal's dynamic value function with quitting options, showing that non-commitment and re-hiring strategies can be optimal, extending principal-agent theory with quitting dynamics.

Findings

Self-enforcing contracts are often suboptimal.

The standard committed-agent contract may be suboptimal with multiple agent types.

The principal will only see finitely many agent quittings due to costs.

Abstract

In this paper we consider a principal agent problem where the agent is allowed to quit, by incurring a cost. When the current agent quits the job, the principal will hire a new one, possibly with a different type. We characterize the principal's dynamic value function, which could be discontinuous at the boundary, as the (unique) minimal solution of an infinite dimensional system of HJB equations, parametrized by the agent's type. This dynamic problem is time consistent in certain sense. Some interesting findings are worth mentioning. First, self-enforcing contracts are typically suboptimal. The principal would rather let the agent quit and hire a new one. Next, the standard contract for a committed agent may also be suboptimal, due to the presence of different types of agents in our model. The principal may prefer no commitment from the agent, then she can hire a cheaper one from the market at a later time by designing the contract to induce the current agent to quit. Moreover, due to the cost incurring to the agent, the principal will see only finitely many quittings.