Note on solving one-to-one matching models with linear transferable utility

We derive a system of fixed-point equations for the equilibrium transfers in a class of one-to-one matching models with linear transferable utility. We then show that, when the degree of substitution between alternatives is bounded from above, the derived system of equations constitutes a contraction mapping. As a result, fixed-point iterations are guaranteed to converge to the unique distribution of equilibrium transfers.