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arXiv · 2302.01498

Equilibrium transport with time-inconsistent costs

Erhan Bayraktar·Bingyan Han
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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.

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Erhan Bayraktar, Bingyan Han. 2023-02-03. Equilibrium transport with time-inconsistent costs. https://doi.org/10.1287/moor.2023.0323

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