交易网络中稳定性的复杂度
Complexity of Stability in Trading Networks
AI总结：
该研究分析交易网络中解概念的计算复杂度，证明更强的稳定性概念的存在性判定、稳定结果存在性判定及结果稳定性验证均为NP难或NP完全问题。
摘要：
高效可计算性是匹配市场中解概念的一项重要性质。我们在代理人偏好满足完全替代性的假设下，研究了交易网络（即带有双边合约的多边匹配市场）中各类解概念的求解与验证的计算复杂度。已知满足轨迹稳定性的结果总是存在，且可在线性时间内找到。本文研究了一个稍强的解概念，该概念下代理人可同时提供一份上游合约和一份下游合约。我们证明，即使在我们模型的特殊（流网络）情形下，判定满足该解概念的结果是否存在也是一个NP完全问题。由此可得，在交易网络（以及流网络）中，稳定结果——即不受任意代理人集合偏离影响的结果——的存在性也是一个NP难问题。最后，我们证明在交易网络中，即便是验证给定结果是否稳定也是NP完全的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
