Contracting with a Learning Agent

Contracting with a Learning Agent

29 Jan 2024 | Guru Guruganesh, Yoav Kolumbus, Jon Schneider, Inbal Talgam-Cohen, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Joshua R. Wang, S. Matthew Weinberg
This paper explores the design of optimal contracts in repeated principal-agent settings, focusing on agents that exhibit no-regret learning. The authors address the challenge of optimizing against a no-regret learner, a problem that is known to be difficult in general games. They achieve an optimal solution for a canonical contract setting where the agent's actions can lead to success or failure. The solution is surprisingly simple: offer the agent a linear contract with a scalar parameter α for a fraction of the time, then switch to a zero contract for the remaining time. This dynamic contract can improve both players' utilities compared to the best static contract. The results are generalized to arbitrary non-linear contracts, provided the principal dynamically scales them. The paper also investigates the impact of uncertainty about the time horizon on the effectiveness of dynamic contracts, showing that the principal's ability to outperform the best static contract diminishes with uncertainty.This paper explores the design of optimal contracts in repeated principal-agent settings, focusing on agents that exhibit no-regret learning. The authors address the challenge of optimizing against a no-regret learner, a problem that is known to be difficult in general games. They achieve an optimal solution for a canonical contract setting where the agent's actions can lead to success or failure. The solution is surprisingly simple: offer the agent a linear contract with a scalar parameter α for a fraction of the time, then switch to a zero contract for the remaining time. This dynamic contract can improve both players' utilities compared to the best static contract. The results are generalized to arbitrary non-linear contracts, provided the principal dynamically scales them. The paper also investigates the impact of uncertainty about the time horizon on the effectiveness of dynamic contracts, showing that the principal's ability to outperform the best static contract diminishes with uncertainty.
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