Trading Networks with Bilateral Contracts

TL;DR

This paper introduces trail stability as a new solution concept for trading networks with bilateral contracts, ensuring stable outcomes under certain conditions and analyzing their properties.

Contribution

It defines trail stability, proves its existence under full substitutability, and explores its properties and relationships with other stability concepts.

Findings

Trail-stable outcomes exist under full substitutability.

Trail stability has a lattice structure and satisfies the rural hospitals theorem.

Weak trail stability is a related, implied concept.

Abstract

We consider a model of matching in trading networks in which firms can enter into bilateral contracts. In trading networks, stable outcomes, which are immune to deviations of arbitrary sets of firms, may not exist. We define a new solution concept called trail stability. Trail-stable outcomes are immune to consecutive, pairwise deviations between linked firms. We show that any trading network with bilateral contracts has a trail-stable outcome whenever firms' choice functions satisfy the full substitutability condition. For trail-stable outcomes, we prove results on the lattice structure, the rural hospitals theorem, strategy-proofness, and comparative statics of firm entry and exit. We also introduce weak trail stability which is implied by trail stability under full substitutability. We describe relationships between the solution concepts.