基于新型交叉效率的资源分配机制

A resource allocation mechanism based on novel cross-efficiency

本文结合数据包络分析(DEA)与合作博弈理论,设计公平合理的资源分配机制.首先建立体现联盟内外部效应的新型交叉效率,这种交叉效率既保留了传统DEA交叉效率的互评本质,又考虑了联盟内部和外部在绩效评价中的差异性,通过赋予决策单元相应的权重,体现联盟内外部不同决策单元重要性的差异;其次,基于新型交叉效率建立合作博弈的特征函数,证明特征函数的超可加性以及相应合作博弈的核心非空性;进一步地,根据特征函数,利用Shapley值设计资源分配机制;最后,通过数值算例和实证分析展现新型交叉效率和权重设置的应用价值.

In this paper,we combine data envelopment analysis(DEA)with cooperative game theory to create a fair resource allocation mechanism in alliances.We introduce a novel crossefficiency measure that considers both internal and external effects within alliances.Weight assignments are used to reflect the importance of internal and external DMUs.We establish a cooperative game characteristic function based on this cross-efficiency,show the super-additivity of the characteristic function and prove the core non-emptiness of the cooperative game.Finally,we design a resource allocation mechanism using the Shapley value based on the characteristic function and demonstrate its practical application through a numerical example and an empirical analysis.