Optimal Decision Making Under Strategic Behavior

Abstract

We are witnessing an increasing use of data-driven predictive models to inform decisions in high-stakes situations, from lending and hiring to university admissions. 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. First, we characterize how strategic investment of effort by individuals leads to a change in the feature distribution. Using this characterization, we show that, in general, optimal decision policies are hard to find 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, we develop an iterative search algorithm that is guaranteed to converge to locally optimal decision policies. 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. This paper was accepted by Vivek Farias, data science. Funding: This work was supported by Machine Learning Cluster of Excellence [EXC #2064/1, Project #390727645], H2020 European Research Council [Grant 945719], and Bundesministerium für Bildung und Forschung [Grant 01IS18039B]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.02567