When reasoning about strategic behavior in a machine learning context it is tempting to combine standard microfoundations of rational agents with the statistical decision theory underlying classification. In this work, we argue that a direct combination of these standard ingredients leads to brittle solution concepts of limited descriptive and prescriptive value. First, we show that rational agents with perfect information produce discontinuities in the aggregate response to a decision rule that we often do not observe empirically. Second, when any positive fraction of agents is not perfectly strategic, desirable stable points---where the classifier is optimal for the data it entails---cease to exist. Third, optimal decision rules under standard microfoundations maximize a measure of negative externality known as social burden within a broad class of possible assumptions about agent behavior.Recognizing these limitations we explore alternatives to standard microfoundations for binary classification. To navigate the space of possible assumptions about how agents respond to a decision rule we specify a set of desiderata our model should satisfy and that help mitigate the limitations of the standard model. We propose noisy response as a promising candidate model. Inspired by smoothed analysis and empirical observations, noisy response incorporates natural imperfection in the agent responses. This model retains analytical tractability, leads to more robust insights about stable points, and imposes a lower social burden at optimality.