Using results from convex analysis, we investiate a novel approach to identification and estimation of discrete choice models which we call the "Mass Transport Approach" (MTA).  We show that the conditional choice probabilities and the choice-specific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem.  Based on this, we propose a new two-step estimator for these models; interestingly, the first step of our estimator involves solving a linear program which is identical to the classic assignment (two-sided matching) game of Shapley and Shubik (1971).  The application of convex-analytic tools to dynamic discrete choice models, and the connection with two-sided matching models, is new in the literature.