Faced with data-driven policies, individuals will manipulate their features to obtain favorable decisions. While earlier works cast these manipulations as undesirable gaming, recent works have adopted a more nuanced causal framing in which manipulations can improve outcomes of interest, and setting coherent mechanisms requires accounting for both predictive accuracy and improvement of the outcome. Typically, these works focus on known causal graphs, consisting only of an outcome and its parents. In this paper, we introduce a general framework in which an outcome and n observed features are related by an arbitrary unknown graph and manipulations are restricted by a fixed budget and cost structure. We develop algorithms that leverage strategic responses to discover the causal graph in a finite number of steps. Given this graph structure, we can then derive mechanisms that trade off between accuracy and improvement. Altogether, our work deepens links between causal discovery and incentive design and provides a more nuanced view of learning under causal strategic prediction.

翻译：面对基于数据驱动的政策，个体将操纵自身特征以获得有利决策。早期研究将此类操纵视为不良博弈，而近期研究则采用了更细致的因果框架，其中操纵能改善目标结果，且制定连贯机制需同时兼顾预测准确性与结果提升。通常，这些研究聚焦于仅包含结果变量及其父节点的已知因果图。本文提出一个通用框架，其中结果变量与n个观测特征通过任意未知图相关联，操纵行为受固定预算和成本结构限制。我们开发了利用策略性响应在有限步骤内发现因果图的算法。给定该图结构后，即可推导出在准确性与改进间权衡的机制。总体而言，本研究深化了因果发现与激励设计之间的关联，并为因果策略预测情境下的学习提供了更细致的视角。