“Optimal Self-Enforcing and Termination” by Cheng Wang
Fudan University & Iowa State University
Shanghai University of Finance and Economics
We study a dynamic principal-agent relationship in which 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 to an external market to hire a new agent. We treat self-enforcing as a choice variable by letting the principal respond strategically to the agent's outside offers. Starting initially from a sufficiently low expected utility of the agent (so the commitment constraint is binding, initially), the continuation of the optimal contract converges to Burdett (1978) where each period the agent quits whenever his outside offer is above the utility the current principal offers, and he stays to receive the same constant expected utility otherwise. On the path of convergence, termination occurs whenever the agent's outside offer exceeds a constant ceiling, and the principal acts to match the agent's outside offer if it is below that constant ceiling but better than his current promised utility. The convergence is monotonic. Conditional on continuation, over time the agent's expected utility converges monotonically to its limiting level while the commitment constraint binds monotonically less; and the limiting utility of the agent is the lowest level of his expected utility at which the commitment constraint is not binding.