This paper studies algorithmic decision-making under human's strategic behavior, where a decision maker uses an algorithm to make decisions about human agents, and the latter with information about the algorithm may exert effort strategically and improve to receive favorable decisions. Unlike prior works that assume agents benefit from their efforts immediately, we consider realistic scenarios where the impacts of these efforts are persistent and agents benefit from efforts by making improvements gradually. We first develop a dynamic model to characterize persistent improvements and based on this construct a Stackelberg game to model the interplay between agents and the decision-maker. We analytically characterize the equilibrium strategies and identify conditions under which agents have incentives to improve. With the dynamics, we then study how the decision-maker can design an optimal policy to incentivize the largest improvements inside the agent population. We also extend the model to settings where 1) agents may be dishonest and game the algorithm into making favorable but erroneous decisions; 2) honest efforts are forgettable and not sufficient to guarantee persistent improvements. With the extended models, we further examine conditions under which agents prefer honest efforts over dishonest behavior and the impacts of forgettable efforts.

翻译：本文研究人类策略行为下的算法决策问题——决策者使用算法对人类主体进行决策，而掌握算法信息的主体可策略性地付出努力并逐步改进以获取有利决策。不同于既有研究假设主体能立即从努力中获益，本文考虑努力效果具有持续性的现实场景，主体通过逐步改进实现受益。我们首先构建刻画持续性改进的动态模型，并在此基础上建立描述主体与决策者博弈关系的斯塔克尔伯格模型。通过解析表征均衡策略，我们识别了主体具有改进动力的条件。基于动态特性，我们进一步研究决策者如何设计最优政策以激励主体群体实现最大改进。此外，我们将模型扩展至两类场景：1）主体可能采取不诚信行为，诱导算法做出有利但错误的决策；2）诚实努力具有可遗忘性，不足以确保持续性改进。基于扩展模型，我们深入探究主体在诚实努力与非诚信行为间的偏好条件，以及可遗忘性努力的影响机制。