29 Jan 2024 | Guru Guruganesh, Yoav Kolumbus, Jon Schneider, Inbal Talgam-Cohen, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Joshua R. Wang, S. Matthew Weinberg
This paper studies repeated contracts with a learning agent, focusing on agents who achieve no-regret outcomes. The authors show that in a canonical contract setting where the agent's choice among multiple actions leads to success/failure, the optimal dynamic contract is surprisingly simple: initially offer a linear contract with scalar α > 0, then switch to a linear contract with scalar 0. This switch causes the agent to "free-fall" through their action space, during which time the principal receives non-zero reward at zero cost. Despite apparent exploitation of the agent, this dynamic contract can leave both players better off compared to the best static contract. The results generalize beyond success/failure to arbitrary non-linear contracts which the principal rescales dynamically. The paper also quantifies the dependence of results on knowledge of the time horizon and is the first to address this consideration in the study of strategizing against learning agents. The authors show that in the linear contract setting, free-fall contracts are optimal dynamic contracts. They also show that dynamic contracts that are optimal for the principal can improve the utilities for both players compared to their utilities under the best static contract. The paper concludes that in arbitrary contract settings, there is a free-fall contract that is optimal among dynamic contracts.This paper studies repeated contracts with a learning agent, focusing on agents who achieve no-regret outcomes. The authors show that in a canonical contract setting where the agent's choice among multiple actions leads to success/failure, the optimal dynamic contract is surprisingly simple: initially offer a linear contract with scalar α > 0, then switch to a linear contract with scalar 0. This switch causes the agent to "free-fall" through their action space, during which time the principal receives non-zero reward at zero cost. Despite apparent exploitation of the agent, this dynamic contract can leave both players better off compared to the best static contract. The results generalize beyond success/failure to arbitrary non-linear contracts which the principal rescales dynamically. The paper also quantifies the dependence of results on knowledge of the time horizon and is the first to address this consideration in the study of strategizing against learning agents. The authors show that in the linear contract setting, free-fall contracts are optimal dynamic contracts. They also show that dynamic contracts that are optimal for the principal can improve the utilities for both players compared to their utilities under the best static contract. The paper concludes that in arbitrary contract settings, there is a free-fall contract that is optimal among dynamic contracts.