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

Optimal Decision Making Under Strategic Behavior