Mini-Lecture: Matching in Trading Networks
This lecture studies matching in trading networks formed through bilateral contracts.
With imperfectly transferable utility, full substitutability of preferences guarantees the existence of outcomes with limited stability properties and — when transfers are continuous and compensating variations are bounded — the existence of competitive equilibria. However, competitive equilibria and weakly stable outcomes need not be efficient.
Under quasi-linear utilities and continuous transfers, full substitutability is sufficient to ensure the existence of stable outcomes for any underlying network structure. In this environment, the sets of stable outcomes and competitive equilibria essentially coincide, and all stable outcomes are efficient.
While full substitutability is necessary, in a maximal-domain sense, for the existence of stable outcomes and competitive equilibria on Cartesian domains, recent work shows that existence can be restored on certain non-Cartesian domains beyond the fully substitutable case.