The DEA Game Cross-Efficiency Model and Its Nash Equilibrium

• Published in: Operations research Vol. 56; no. 5; pp. 1278 - 1288
• Main Authors: Liang, Liang, Wu, Jie, Cook, Wade D, Zhu, Joe
• Format: Journal Article
• Language: English
• Published: Hanover, MD INFORMS 01.09.2008; Institute for Operations Research and the Management Sciences
• Subjects: Analysis; Applied sciences; Continuous functions; cross efficiency; Data envelopment analysis; data envelopment analysis (DEA); Decision making; Decision theory. Utility theory; Economic competition; Efficiency; Efficiency metrics; Equilibrium; Exact sciences and technology; Firm modelling; game; Game theory; Mathematics; Modeling; Nash equilibrium; Nonparametric inference; Objective functions; Operational research and scientific management; Operational research. Management science; Political candidates; Preferential voting; Probability and statistics; Sciences and techniques of general use; Statistics; Studies; Voting; United States; Performance evaluation; game; Decision support system; Decision making; Nash equilibrium; Non parametric estimation; Modeling; Equilibrium point; data envelopment analysis (DEA); Multiplier; Game equilibrium; Occupation time; cross efficiency; Data envelopment analysis
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1070.0487

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.