Equilibrium transport with time-inconsistent costs

TL;DR

This paper introduces the concept of equilibrium transport for time-inconsistent costs in sequential data, establishing existence and uniqueness results, and applying the framework to various economic and statistical problems.

Contribution

It develops a novel equilibrium transport framework for time-inconsistent preferences, with existence and uniqueness proofs in complex settings, extending optimal transport theory.

Findings

Existence of equilibrium transport in semi-discrete and continuous cases.

Uniqueness of equilibrium transport in the non-Markovian case.

Numerical results show a positive link between mismatches and state dependence.

Abstract

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 semi-discrete Markovian case and the continuous non-Markovian case with strict quasiconvexity, while 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.