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：面对数据驱动的政策，个体将操纵其特征以获得有利的决策。尽管早期研究将这些操纵视为不良博弈，但近期研究采用了更细致的因果框架，其中操纵可以改善感兴趣的结果，而制定连贯的机制需要同时考虑预测准确性和结果的改进。通常，这些研究侧重于已知的因果图，仅包含一个结果及其父节点。在本文中，我们引入了一个通用框架，其中结果和n个观察到的特征通过任意未知图相关联，且操纵受固定预算和成本结构约束。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。在获得该图结构后，我们能够推导出在准确性与改进之间权衡的机制。总体而言，我们的工作加深了因果发现与激励设计之间的联系，并为因果策略预测下的学习提供了更细致的视角。