Complexity of stability in trading networks

Tamás Fleiner (), Zsuzsanna Jankó (), Ildikó Schlotter () and Alexander Teytelboym ()
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Tamás Fleiner: Budapest University of Technology and Economics
Zsuzsanna Jankó: Centre for Economic and Regional Studies
Ildikó Schlotter: Budapest University of Technology and Economics
Alexander Teytelboym: University of Oxford

International Journal of Game Theory, 2023, vol. 52, issue 3, No 1, 629-648

Abstract: 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.

Keywords: Matching markets; Market design; Computational complexity; Trading networks; Flow networks; Supply chains; Trail stability; Chain stability; Stability; Contracts (search for similar items in EconPapers)
JEL-codes: C78 L14 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00182-022-00833-0

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