Using results from Convex Analysis, we investigate a novel approach to identification and estimation of discrete-choice models that we call the mass transport approach . 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 that 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. Monte Carlo results demonstrate the good performance of this estimator, and we provide an empirical application based on Rust's (1987) bus engine replacement model.