When learning is used to inform decisions about humans, such as for loans, hiring, or admissions, this can incentivize users to strategically modify their features, at a cost, to obtain positive predictions. The common assumption is that the function governing costs is exogenous, fixed, and predetermined. We challenge this assumption, and assert that costs emerge as a result of deploying a classifier. Our idea is simple: when users seek positive predictions, this creates demand for important features; and if features are available for purchase, then a market will form, and competition will give rise to prices. We extend the strategic classification framework to support this notion, and study learning in a setting where a classifier can induce a market for features. We present an analysis of the learning task, devise an algorithm for computing market prices, propose a differentiable learning framework, and conduct experiments to explore our novel setting and approach.

When users stand to gain from certain predictive outcomes, they are prone to act strategically to obtain predictions that are favorable. Most current works consider strategic behavior that manifests as users modifying their features; instead, we study a novel setting in which users decide whether to even participate (or not), this in response to the learned classifier. Considering learning approaches of increasing strategic awareness, we investigate the effects of user self-selection on learning, and the implications of learning on the composition of the self-selected population. Building on this, we propose a differentiable framework for learning under self-selective behavior, which can be optimized effectively. We conclude with experiments on real data and simulated behavior that complement our analysis and demonstrate the utility of our approach.