Contracting with a Learning Agent

Real-life contractual relations typically involve repeated interactions between the principal and agent, where, despite theoretical appeal, players rarely use complex dynamic strategies and instead manage uncertainty through learning algorithms.In this paper, we initiate the study of repeated contracts with learning agents, focusing on those achieving no-regret outcomes. For the canonical setting where the agent’s actions result in success or failure, we present a simple, optimal solution for the principal: Initially provide a linear contract with scalar $\alpha > 0$, then switch to a zero-scalar contract. This shift causes the agent to “free-fall” through their action space, yielding non-zero rewards for the principal at zero cost. Interestingly, despite the apparent exploitation, there are instances where our dynamic contract can make \emph{both} players better off compared to the best static contract. We then broaden the scope of our results to general linearly-scaled contracts, and, finally, to the best of our knowledge, we provide the first analysis of optimization against learning agents with uncertainty about the time horizon.