# Optimal Decision Making Under Strategic Behavior

arXiv: https://arxiv.org/abs/1905.09239 · HTML: https://mlsanity.com/paper/1905.09239/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2019.

## Built on by (most cited first, 20 of 20)

- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization](https://mlsanity.com/paper/2106.09082/) (2021)
- [Learnability Gaps of Strategic Classification](https://mlsanity.com/paper/2402.19303/) (2024)
- [A Classification of Feedback Loops and Their Relation to Biases in Automated Decision-Making Systems](https://mlsanity.com/paper/2305.06055/) (2023)
- [Bayesian Strategic Classification](https://mlsanity.com/paper/2402.08758/) (2024)
- [Measuring Fairness Under Unawareness of Sensitive Attributes: A Quantification-Based Approach](https://mlsanity.com/paper/2109.08549/) (2021)
- [Sequential Strategic Screening](https://mlsanity.com/paper/2301.13397/) (2023)
- [The Risks of Recourse in Binary Classification](https://mlsanity.com/paper/2306.00497/) (2023)
- [Learning under Imitative Strategic Behavior with Unforeseeable Outcomes](https://mlsanity.com/paper/2405.01797/) (2024)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Practical Performative Policy Learning with Strategic Agents](https://mlsanity.com/paper/2412.01344/) (2024)
- [Microfoundation Inference for Strategic Prediction](https://mlsanity.com/paper/2411.08998/) (2024)
- [To Give or Not to Give? The Impacts of Strategically Withheld Recourse](https://mlsanity.com/paper/2504.05891/) (2025)
- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)
- [On the Stochastic (Variance-Reduced) Proximal Gradient Method for Regularized Expected Reward Optimization](https://mlsanity.com/paper/2401.12508/) (2024)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)
- [A Short Survey of Systematic Generalization](https://mlsanity.com/paper/2211.11956/) (2022)
- [Partial Fairness Awareness: Belief-Guided Strategic Mechanism for Strategic Agents](https://mlsanity.com/paper/2606.00826/) (2026)
- [Robust Strategic Classification under Decision-Dependent Cost Uncertainty](https://mlsanity.com/paper/2606.30136/) (2026)

## Abstract (arXiv)

We are witnessing an increasing use of data-driven predictive models to inform decisions. As decisions have implications for individuals and society, there is increasing pressure on decision makers to be transparent about their decision policies. At the same time, individuals may use knowledge, gained by transparency, to invest effort strategically in order to maximize their chances of receiving a beneficial decision. Our goal is to find decision policies that are optimal in terms of utility in such a strategic setting. To this end, we first characterize how strategic investment of effort by individuals leads to a change in the feature distribution. Using this characterization, we first show that, in general, we cannot expect to find optimal decision policies in polynomial time and there are cases in which deterministic policies are suboptimal. Then, we demonstrate that, if the cost individuals pay to change their features satisfies a natural monotonicity assumption, we can narrow down the search for the optimal policy to a particular family of decision policies with a set of desirable properties, which allow for a highly effective polynomial time heuristic search algorithm using dynamic programming. Finally, under no assumptions on the cost individuals pay to change their features, we develop an iterative search algorithm that is guaranteed to find locally optimal decision policies also in polynomial time. Experiments on synthetic and real credit card data illustrate our theoretical findings and show that the decision policies found by our algorithms achieve higher utility than those that do not account for strategic behavior.