The structure of equilibria in trading networks with frictions

Abstract

Several structural results for the set of competitive equilibria in trading networks with frictions are established: The lattice theorem, the rural hospitals theorem, the existence of side‐optimal equilibria, and a group‐incentive‐compatibility result hold with imperfectly transferable utility and in the presence of frictions. While our results are developed in a trading network model, they also imply analogous (and new) results for exchange economies with combinatorial demand and for two‐sided matching markets with transfers.

The Equilibrium Existence Duality

“…D of Fleiner et al (2019). Kelso and Crawford (1982) imposed a gross substitutability condition at all price vectors-instead of only price vectors at which demand is single valued-which leads to a strictly stronger condition in the presence of income effects (Schlegel 2022), even when at most one unit of each good is demanded. 21 Fleiner et al (2019) worked with a matching model and considered competitive equilibrium with personalized pricing, but their arguments also apply in exchange economies without personalized pricing.…”

“…21 Fleiner et al (2019) worked with a matching model and considered competitive equilibrium with personalized pricing, but their arguments also apply in exchange economies without personalized pricing. See also Schlegel (2022). 22 Danilov, Koshevoy, and Murota (2001, example 2) also showed the connection between Quinzii's (1984) housing market economy and a substitutability condition but formulated their discussion in terms of the shape of the convex hull at domains at which demand is multivalued instead of net substitutability.…”