sg 16(11): e1

Research Article

Trading networks with bilateral contracts

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  • @ARTICLE{10.4108/eai.8-8-2015.2260329,
        author={Tamas Fleiner and Zsuzsanna Janko and Akihisa Tamura and Alexander Teytelboym},
        title={Trading networks with bilateral contracts},
        journal={EAI Endorsed Transactions on Serious Games},
        keywords={matching markets, contracts, networks, supply chains, stability, trail stability, competitive equilibrium},
  • Tamas Fleiner
    Zsuzsanna Janko
    Akihisa Tamura
    Alexander Teytelboym
    Year: 2015
    Trading networks with bilateral contracts
    DOI: 10.4108/eai.8-8-2015.2260329
Tamas Fleiner1, Zsuzsanna Janko2, Akihisa Tamura3, Alexander Teytelboym4,*
  • 1: BME SZIT
  • 2: ELTE, Oper. Res. Dept.
  • 3: Keio University, Dept. of Math.
  • 4: INET, University of Oxford
*Contact email:


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.