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Complexity of stability in trading networks

Author

Listed:
  • Tamás Fleiner

    (Budapest University of Technology and Economics
    Centre for Economic and Regional Studies)

  • Zsuzsanna Jankó

    (Centre for Economic and Regional Studies
    Corvinus University of Budapest)

  • Ildikó Schlotter

    (Budapest University of Technology and Economics
    Centre for Economic and Regional Studies)

  • Alexander Teytelboym

    (University of Oxford)

Abstract

Efficient computability is an important property of solution concepts. We consider the computational complexity of finding and verifying various solution concepts in trading networks—multi-sided matching markets with bilateral contracts and without transferable utility—under the assumption of full substitutability of agents’ preferences. It is known that outcomes that satisfy trail stability always exist and can be found in linear time. However, we show that the existence of stable outcomes—immune to deviations by arbitrary sets of agents—is an $${{\textsf{N}}}{{\textsf{P}}}$$ N P -hard problem in trading networks. We also show that even verifying whether a given outcome is stable is $${{\textsf{N}}}{{\textsf{P}}}$$ N P -hard in trading networks.

Suggested Citation

  • Tamás Fleiner & Zsuzsanna Jankó & Ildikó Schlotter & Alexander Teytelboym, 2023. "Complexity of stability in trading networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 629-648, September.
    • Handle: RePEc:spr:jogath:v:52:y:2023:i:3:d:10.1007_s00182-022-00833-0
    DOI: 10.1007/s00182-022-00833-0
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    References listed on IDEAS

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    More about this item

    Keywords

    Matching markets; Market design; Computational complexity; Trading networks; Flow networks; Supply chains; Trail stability; Chain stability; Stability; Contracts;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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