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Barycenters in the Wasserstein Space (2011, methodology): “Our interest in interpolating between more than two probability measures by minimizing an averaged sum of squared Wasserstein distances originated from the recent papers in mathematical economics by Carlier and Ekeland [4], and Chiappori, McCann and Nesheim [5] who studied matching and hedonic prici”
Multi-marginal optimal transport: theory and applications (2014, methodology): “A different notion of purity, essentially that workers of the same type x1 always buy goods of the same type y ∈ Y was discussed by Carlier and Ekeland, and requires only twistedness of the first cost c1 [13].”
Wasserstein Barycenters over Riemannian manifolds (2014, methodology): “Moreover, applying 1 and 2 to a result of Carlier-Ekeland [8, Proof of Proposition 3], we get ν := xλ#γ is the unique Wasserstein barycenter measure of the measures µ1, ..., µm with weights λi.”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, background): “For instance, in economics (see [109]), one can think at contracts with more than two agents (when a seller given a good to a buyer in exchange of money, this is a contract between two agents; when somebody wants to build a house, he buys some land and hires a carpenter and an architect, there are a”