我们研究了当委托人对代理人可采取的行动仅掌握有限信息时的稳健合约设计问题。委托人根据不确定行动空间所导致的最坏情形绩效来评估一份合约。Carroll（AER 2015）证明，线性合约在确定性合约中是最优的。最近，Kambhampati（JET 2023）证明，通过在线性合约之间进行随机化，可以严格提高委托人的收益。在本文中，我们刻画了最优随机化合约；该合约仍保持线性，并且其累积密度函数具有闭式形式。即使委托人只知道代理人的一个非平凡行动，随机化合约相对于确定性合约的优势也可以任意大。此外，我们的结果可推广到由 Dai 和 Toikka（Econometrica 2022）提出的团队缔约模型。
英文摘要：
We consider the robust contract design problem when the principal only has limited information about the actions the agent can take. The principal evaluates a contract according to its worst-case performance caused by the uncertain action space. Carroll (AER 2015) showed that a linear contract is optimal among deterministic contracts. Recently, Kambhampati (JET 2023) showed that the principal's payoff can be strictly increased via randomization over linear contracts. In this paper, we characterize the optimal randomized contract, which remains linear and admits a closed form of its cumulative density function. The advantage of randomized contracts over deterministic contracts can be arbitrarily large even when the principal knows only one non-trivial action of the agent. Furthermore, our result generalizes to the model of contracting with teams, by Dai and Toikka (Econometrica 2022).
Paid with Models: Optimal Contract Design for Collaborative Machine Learning
Institute of Data Science, National University of Singapore（新加坡国立大学数据科学研究院）；Singapore-MIT Alliance for Research and Technology（新加坡-麻省理工研究与技术联盟）；Department of Computer Science, National University of Singapore（新加坡国立大学计算机科学系）
