Trading networks with bilateral contracts

• Main Authors: Tamas Fleiner, Zsuzsanna Janko, Akihisa Tamura, Alexander Teytelboym
• Format: Article
• Language: English
• Published: European Alliance for Innovation (EAI) 2016-12-01
• Series: EAI Endorsed Transactions on Serious Games
• Subjects: matching markets; contracts; networks; supply chains; stability; trail stability; competitive equilibrium
• Online Access: http://eudl.eu/doi/10.4108/eai.8-8-2015.2260329

We study production networks in which firms match and sign bilateral contracts. Firms can buy from and sell to one another directly or via intermediaries. It is well-known that in this case group-stable outcomes might not exist. We show that the problem of determining whether an allocation is group-stable is NP-hard. We define a new stability concept, called trail stability, and show that any network of bilateral contracts has a trail-stable outcome whenever agents' preferences satisfy full substitutability. Trail-stable outcomes rule out consecutive and consistent pairwise blocks that form trails of contracts. Trail stability is a natural extension of chain stability and is a stronger solution concept in general contract networks. Trail-stable outcomes may not be immune to group deviations or efficient. In fact, we show that outcomes satisfying an even more demanding stability property -- full trail stability -- always exist. Fully trail-stable outcomes also rule out trail blocks, but an intermediary is not required to choose all contracts in the trail -- only local upstream-downstream pairs. We pin down conditions under which terminal contracts in trail-stable and fully trail-stable outcomes have a lattice structure. We describe the relationships between all stability concepts. When contracts specify trades and prices, we also show that trail-stable competitive equilibrium outcomes exist in networked markets even when agents' utility functions are not quasilinear.