Automated decision-making tools increasingly assess individuals to determine if they qualify for high-stakes opportunities. A recent line of research investigates how strategic agents may respond to such scoring tools to receive favorable assessments. While prior work has focused on the short-term strategic interactions between a decision-making institution (modeled as a principal) and individual decision-subjects (modeled as agents), we investigate interactions spanning multiple time-steps. In particular, we consider settings in which the agent's effort investment today can accumulate over time in the form of an internal state - impacting both his future rewards and that of the principal. We characterize the Stackelberg equilibrium of the resulting game and provide novel algorithms for computing it. Our analysis reveals several intriguing insights about the role of multiple interactions in shaping the game's outcome: First, we establish that in our stateful setting, the class of all linear assessment policies remains as powerful as the larger class of all monotonic assessment policies. While recovering the principal's optimal policy requires solving a non-convex optimization problem, we provide polynomial-time algorithms for recovering both the principal and agent's optimal policies under common assumptions about the process by which effort investments convert to observable features. Most importantly, we show that with multiple rounds of interaction at her disposal, the principal is more effective at incentivizing the agent to accumulate effort in her desired direction. Our work addresses several critical gaps in the growing literature on the societal impacts of automated decision-making - by focusing on longer time horizons and accounting for the compounding nature of decisions individuals receive over time.

中文翻译：

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状态策略回归

自动化决策工具越来越多地评估个人以确定他们是否有资格获得高风险机会。最近的一项研究调查了战略代理人如何对此类评分工具做出反应以获得有利的评估。虽然之前的工作侧重于决策机构（建模为委托人）和个体决策主体（建模为代理）之间的短期战略交互，但我们研究了跨越多个时间步长的交互。特别是，我们考虑了代理今天的努力投资可以以内部状态的形式随时间累积的设置——影响他和委托人的未来回报。我们描述了结果博弈的 Stackelberg 均衡，并提供了计算它的新算法。我们的分析揭示了关于多重交互在塑造游戏结果中的作用的几个有趣的见解：首先，我们确定，在我们的状态设置中，所有线性评估策略的类别仍然与所有单调评估策略的较大类别一样强大。虽然恢复委托人的最优策略需要解决非凸优化问题，但我们提供多项式时间算法，用于在关于努力投资转换为可观察特征的过程的共同假设下恢复委托人和代理人的最优策略。最重要的是，我们表明，通过多轮互动，委托人可以更有效地激励代理人朝着她想要的方向努力。