Dynamic Contract Design with Learning

Abstract

Incentivizing Effort While Learning the Market Condition When a firm hires an agent to generate customers in a new market, neither party initially knows whether the market is favorable. In “Dynamic Contract Design with Learning,” Wang, Liang, and Sun study the interaction between learning and moral hazard: effort is costly and unobservable, so a missing arrival may reflect an unfavorable market, bad luck, or shirking. The firm’s goal is to design a dynamic contract governing arrival-based payments and termination, thereby motivating effort while learning whether to continue. Yet shirking can make the principal more pessimistic than the agent and create scope to manipulate future payments. The authors prove that an optimal contract inducing full effort until termination exists, but computing it appears prohibitively complex. They develop two simple online contracts with payments and termination thresholds fixed in advance. Both induce full effort and achieve O(ln T) regret over T periods against a first-best, full-information benchmark. A matching Ω(ln T) lower bound proves rate optimality. The results extend to continuous time and differing prior beliefs.