Optimal Self-Enforcement and Termination

We study a dynamic principal-agent problem where the agent receives a stochastic outside opportunity/offer each period and he cannot commit to not leaving the ongoing relationship. Termination, while costly, allows the principal to go back to an external market to hire a new agent. We treat self-enforcement and termination both as endogenous variables and let the principal respond strategically to the agent's outside offers. The optimal contract is either dynamic or stationary. If it starts with a sufficiently low expected utility for the agent, then the principal matches the agent's outside offer to retain him whenever the value of the outside offer is above his current expected utility but below a constant cutoff for termination, and the agent is terminated whenever the value of the outside offer exceeds that constant cutoff. If the optimal contract starts the agent with a sufficiently high expected utility, then it is stationary: the agent's expected utility is constant conditional on retention, and he is terminated once he receives an outside offer higher than a constant cutoff for termination. The stationary optimal contract generates both voluntary and involuntary terminations. All dynamic optimal contracts converge stochastically but monotonically to a single stationary optimal contract.

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