Impatience vs. Incentives

This paper studies the long-run dynamics of Pareto-optimal self-enforcing contracts in a repeated principal-agent framework with differential discounting. In such a setting, impatience concerns encourage contracts to favor the patient player in the long run and incentive concerns encourage contracts to favor the agent in the long run. When these two forces are aligned or one is relatively strong, we show that every Pareto-optimal self-enforcing contract converges to a steady state in the long run in a well-behaved way. In particular, the results of Ray (2002) and Lehrer and Pauzner (1999) can be recovered as limiting cases. However, when the forces are opposed and of comparable strength, our main result is that some Paretooptimal self-enforcing contracts deterministically oscillate between agent-preferred and principal-preferred states. Oscillation may be damped so that in the long run a steady state is reached; or explosive until the allocation reaches one of the participation constraints and then alternates between a pair of states forever. ∗We thank Peter DeMarzo, Mike Fishman, Willie Fuchs, Drew Fudenberg, Nicolae Garleanu, Milton Harris, Rich Kihlstrom, Natalia Kovrijnykh, Jonathan Levin, Andrey Malenko, John Morgan and Bilge Yilmaz for helpful comments. †University of California, Berkeley (Haas), email: [email protected]. ‡University of Pennsylvania, Wharton, e-mail: [email protected].