Complexity of Stability in Trading Networks

Tamás Fleiner; Zsuzsanna Jankó; Ildikó Schlotter; Alexander Teytelboym

doi:10.1007/s00182-022-00833-0

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arXiv · 1805.08758

Complexity of Stability in Trading Networks

Tamás Fleiner·Zsuzsanna Jankó·Ildikó Schlotter·Alexander Teytelboym

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Abstract

Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with bilateral contracts-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. Here we consider a slightly stronger solution concept in which agents can simultaneously offer an upstream and a downstream contract. We show that deciding the existence of outcomes satisfying this solution concept is an NP-complete problem even in a special (flow network) case of our model. It follows that the existence of stable outcomes--immune to deviations by arbitrary sets of agents-is also an NP-hard problem in trading networks (and in flow networks). Finally, we show that even verifying whether a given outcome is stable is NP-complete in trading networks.

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BibTeX RIS

Tamás Fleiner, Zsuzsanna Jankó, Ildikó Schlotter, Alexander Teytelboym. 2018-05-22. Complexity of Stability in Trading Networks. https://doi.org/10.1007/s00182-022-00833-0

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