# Trading Networks with Bilateral Contracts

arXiv: https://arxiv.org/abs/1510.01210 · HTML: https://mlsanity.com/paper/1510.01210/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2015.

## Built on by (most cited first, 1 of 1)

- [Online Bidding Algorithms for Return-on-Spend Constrained Advertisers](https://mlsanity.com/paper/2208.13713/) (2022)

## Abstract (arXiv)

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.