Stability in Tranding Networks
summary
Defines trail-stability as immunity to consecutive pairwise deviations along a directed trail and proves existence whenever firms’ choice functions satisfy full substitutability plus IRC, by constructing a monotone operator and applying Tarski fixed point. Shows path/cycle (and hence stable) outcomes can fail to exist with cycles, gives a flow-network NP-completeness reduction, and proves both deciding existence of a stable outcome and verifying that a given outcome is stable are NP-hard/NP-complete. Notes buyer-/seller-optimal trail-stable outcomes and lattice-type comparisons under extra conditions.
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