The DEA Game Cross-Efficiency Model and Its Nash Equilibrium



     长期以来，DEA研究一直将决策单元看成是一个“黑箱”。只分析这个“黑箱”外部的输入和输出，严重限制了DEA的研究内容和应用范围。一个组织的运行方式、体制结构等内部因素都会对其效率产生重要的影响，DEA研究理应“打开黑箱”。对于如何破解“黑箱”内部的奥秘，作者想到一种自己所熟悉和掌握的路径——博弈论。“DEA分析组织效率时，决策单元内部和不同决策单元之间就是一个博弈的过程。”



            In this paper, we examine the cross-efficiency concept in data envelopment analysis (DEA). Cross efficiency links one decision-making unit's (DMU) performance with others and has the appeal that scores arise from peer evaluation. However, a number of the current cross-efficiency approaches are flawed because they use scores that are arbitrary in that they depend on a particular set of optimal DEA weights generated by the computer code in use at the time. One set of optimal DEA weights (possibly out of many alternate optima) may improve the cross efficiency of some DMUs, but at the expense of others. While models have been developed that incorporate secondary goals aimed at being more selective in the choice of optimal multipliers, the alternate optima issue remains. In cases where there is competition among DMUs, this situation may be seen as undesirable and unfair. To address this issue, this paper generalizes the original DEA cross-efficiency concept to game cross efficiency. Specifically, each DMU is viewed as a player that seeks to maximize its own efficiency, under the condition that the cross efficiency of each of the other DMUs does not deteriorate. The average game cross-efficiency score is obtained when the DMU's own maximized efficiency scores are averaged. To implement the DEA game cross-efficiency model, an algorithm for deriving the best (game cross-efficiency) scores is presented. We show that the optimal game cross-efficiency scores constitute a Nash equilibrium point.