Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2013), Article ID 747596, 8 pages.

Game Cross Efficiency for Systems with Two-Stage Structures

Chaoqun Ma, Debin Liu, Zhongbao Zhou, Wei Zhao, and Wenbin Liu

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Abstract

Data envelopment analysis (DEA) is a nonparametric approach for measuring the relative efficiencies of peer decision-making units (DMUs). For systems with two-stage structures, where all the outputs from the first stage are the only inputs to the second stage, the centralized model, which is based on the concept of cooperative game theory, has been widely used to examine the efficiencies of such systems. We define the cross efficiencies of systems with two-stage structures. Since the centralized model may lead to multiple and unacceptable cross efficiencies and rankings of DMUs due to its high flexibility in choosing optimal weights on input and output factors, we develop a game model to obtain a unique cross efficiency measure, which is constructed from the perspective of noncooperative game. An iterative algorithm is then proposed to obtain the game cross efficiencies for the overall systems and subsystems. We use the proposed game model to evaluate the performance of top 30 US commercial banks. The results show that the game model can lead to a unique reasonable cross efficiency for each DMU.

Article information

Source
J. Appl. Math. Volume 2014, Special Issue (2013), Article ID 747596, 8 pages.

Dates
First available in Project Euclid: 1 October 2014

Permanent link to this document
http://projecteuclid.org/euclid.jam/1412177642

Digital Object Identifier
doi:10.1155/2014/747596

Mathematical Reviews number (MathSciNet)
MR3178971

Citation

Ma, Chaoqun; Liu, Debin; Zhou, Zhongbao; Zhao, Wei; Liu, Wenbin. Game Cross Efficiency for Systems with Two-Stage Structures. J. Appl. Math. 2014, Special Issue (2013), Article ID 747596, 8 pages. doi:10.1155/2014/747596. http://projecteuclid.org/euclid.jam/1412177642.


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