Equilibrium transport with time-inconsistent costs: An application to matching problems in the job market

Abstract

Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences under a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized optimal transport with general f -divergence. Under the bi-causal constraint, we introduce the concept of equilibrium transport and provide a characterization. We apply our framework to study inertia of two job markets, top-ranking executives and academia. The empirical analysis shows that a job market with stronger inertia is less efficient. The University of California (UC) postdoc job market has the strongest inertia even than that of executives, while there is no evidence of inertia in the UC faculty job market.