Complexity of Stability in Trading Networks
share
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. First, we show that outcomes that satisfy an economically intuitive solution concept---trail stability---always exist and can be found in linear time. Second, 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-complete 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.
READ FULL TEXT