Optimal Transport in Economics
Abstract
Optimal transport provides a common language for allocation, equilibrium, computation, and inference. Its primal problem assigns mass or agents, while its dual variables admit economic interpretations as utilities, prices, and scarcity rents. This review explains why this combination has proved unusually effective in economics. We first present the core results, including Kantorovich duality, integrality, cyclical monotonicity, the canonical distance and quadratic costs, and entropic regularization. We then trace the field's development from planning and operations research to modern analysis, statistics, and computation. The economic literature is organized around two roles for transport: as a model of matching, trade, hedonic equilibrium, and aggregate assignment; and as a tool for coupling distributions, measuring discrepancies, constructing multivariate ranks, solving inverse problems, and certifying economic conclusions. We conclude by examining extensions beyond transferable utility, one-to-one matching, static allocation, and unconstrained transport, together with open questions involving learning and identification across multiple markets.
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BibTeX
@misc{fahli2026optimal,
title = {{Optimal Transport in Economics}},
author = {Amine Fahli and Alfred Galichon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.06277},
eprint = {2609.06277},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06277},
}
RIS
TY - UNPB
TI - Optimal Transport in Economics
AU - Amine Fahli
AU - Alfred Galichon
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2609.06277
UR - https://arxiv.org/abs/2609.06277
AB - Optimal transport provides a common language for allocation, equilibrium, computation, and inference. Its primal problem assigns mass or agents, while its dual variables admit economic interpretations as utilities, prices, and scarcity rents. This review explains why this combination has proved unusually effective in economics. We first present the core results, including Kantorovich duality, integrality, cyclical monotonicity, the canonical distance and quadratic costs, and entropic regularization. We then trace the field's development from planning and operations research to modern analysis, statistics, and computation. The economic literature is organized around two roles for transport: as a model of matching, trade, hedonic equilibrium, and aggregate assignment; and as a tool for coupling distributions, measuring discrepancies, constructing multivariate ranks, solving inverse problems, and certifying economic conclusions. We conclude by examining extensions beyond transferable utility, one-to-one matching, static allocation, and unconstrained transport, together with open questions involving learning and identification across multiple markets.
ER -