This dissertation consists of three essays in the field of microeconomic theory. The first essay “A Revealed Preference Test for Probabilistic Sophistication” provides a test that verifies whether or not observed choices of agents violate the axioms of probabilistic sophistication as defined by Machina and Schmeidler (1992). The second essay “Accounting for Investment in Optimal Dynamic Matching” studies the design of optimal matching policies in dynamic two-sided matching markets where agents have an opportunity to invest in their own match quality. It shows that the optimal policy increases the assortativity of the resulting matches relative to an exogenous-quality baseline and that introducing wasteful delays to low quality agents’ matches may be necessary to encourage the optimal level of investment. The third essay “Computationally Tractable Inference” provides a framework for imposing computational tractability constraints on observed behavior in statistical decision theory. It proves the existence of behavior that cannot be replicated by a computationally tractable algorithm and provides sufficient conditions for a decision problem to generate behavior that can be replicated by such an algorithm.