Many claims about political behavior are based on implicit assumptions about human reasoning. One such assumption, that political actors think in complex and similar ways when assessing strategies, is nested within widely used game theoretic equilibrium concepts. Empirical research casts doubt on the validity of these assumptions in important cases. For example, the finding that some citizens expend limited cognitive energy to social concerns runs counter to the assumption that citizens (e.g., jurors) base all decisions on complex thoughts. Similarly, evidence that some political actors (e.g., Democrats and Republicans) think about political cause-and-effect quite differently runs against the assumption that all players reason about politics in similar ways. The self-confirming equilibrium (SCE) concept provides a means for evaluating the robustness of theoretical conclusions to the introduction of a broad range of psychological assumptions. Through arguments and examples, we explain opportunities and challenges inherent in using the SCE concept. We find that the concept provides an improved foundation for more serious and constructive interactions between formal theoretic and psychology-oriented literatures