Constrained optimal transport with an application to large markets with indivisible goods
This study addresses the optimal transport problem between a continuum of agents and a finite set of discrete options under linear constraints, aiming to rectify a flaw in the existence proof of equilibria in large markets with indivisible goods. By developing a Monge–Kantorovich duality theory tailored to this setting and leveraging tools from functional analysis, convex analysis, and potential function optimization, the authors correct a prior erroneous claim regarding compactness. The main contributions are twofold: first, they rigorously reestablish the existence of market equilibria; second, they characterize equilibrium prices as minimizers of a dual potential function, thereby providing a computationally tractable method for equilibrium computation.