Gaming Helps! Learning from Strategic Interactions in Natural Dynamics

We consider an online regression setting in which individuals adapt to the regression model: arriving individuals may access the model throughout the process, and invest strategically in modifying their own features so as to improve their predicted score. Such feature manipulation, or ``gaming'', has been observed in various scenarios---from credit assessment to school admissions, posing a challenge for the learner. Surprisingly, we find that such strategic manipulation may in fact help the learner recover the meaningful variables in settings where an agent can invest in improving meaningful features---that is, the features that, when changed, affect the true label, as opposed to non-meaningful features that have no effect. We show that even simple behavior on the learner's part allows her to simultaneously i) accurately recover the meaningful features, and ii) incentivize agents to invest in these meaningful features, providing incentives for improvement.