In this talk we consider a principal agent problem where the agent is allowed to quit. When the current agent quits the job, the principal would hire a new agent from the market, possibly with a different type. We shall characterize the principal's dynamic optimal value function through an infinite dimensional HJB equation, parametrized by the agent's type.
Our results show that self-enforcing contracts, which are considered in the standard literature for non-committed agents, are typically too expensive for the principal. Instead of disincentivizing the agent to quit, the principal would prefer to let the agent quit and hire a new one. Moreover, the standard optimal contract for committed agent may also be suboptimal. In some markets, the principal may prefer the agent to quit so that she can hire a cheaper agent. The talk is based on a joint walk with Zimu Zhu.
