Equilibrium Transport with Time-Inconsistent Costs

Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized optimal transport with general f-divergence. Under the bicausal constraint, we introduce the concept of equilibrium transport. Existence is proved in the semidiscrete Markovian case and the continuous non-Markovian case with strict quasiconvexity, whereas uniqueness also holds in the second case. We apply our framework to study mean-variance dynamic matching, nonlinear or state-dependent objectives with Gaussian data, and mismatches in job markets. Numerical results indicate a positive relationship between mismatches and state dependence. Funding: This work was supported by The Hong Kong University of Science and Technology (Guangzhou) Start-up Fund [Grant G0101000197], the National Science Foundation of China [Grant 12401621], the Guangzhou-HKUST(GZ) Joint Funding Program [Grant 2024A03J0630], the National Science Foundation, Division of Mathematical Sciences [Grant DMS-2106556], and the University of Michigan (Susan M. Smith chair). Supplemental Material: The e-companion is available at https://doi.org/10.1287/moor.2023.0323 .