IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2014y2014i1n747596.html

Game Cross Efficiency for Systems with Two‐Stage Structures

Author

Listed:
  • Chaoqun Ma
  • Debin Liu
  • Zhongbao Zhou
  • Wei Zhao
  • Wenbin Liu

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.

Suggested Citation

  • Chaoqun Ma & Debin Liu & Zhongbao Zhou & Wei Zhao & Wenbin Liu, 2014. "Game Cross Efficiency for Systems with Two‐Stage Structures," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:747596
    DOI: 10.1155/2014/747596
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/747596
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/747596?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity and intermediate products: A frontier approach," Economics Letters, Elsevier, vol. 50(1), pages 65-70, January.
    2. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    3. Lawrence M. Seiford & Joe Zhu, 1999. "Profitability and Marketability of the Top 55 U.S. Commercial Banks," Management Science, INFORMS, vol. 45(9), pages 1270-1288, September.
    4. Greg Gregoriou & Fabrice Rouah & Stephen Satchell & Fernando Diz, 2005. "Simple and cross efficiency of CTAs using data envelopment analysis," The European Journal of Finance, Taylor & Francis Journals, vol. 11(5), pages 393-409.
    5. Nakabayashi, Ken & Tone, Kaoru, 2006. "Egoist's dilemma: a DEA game," Omega, Elsevier, vol. 34(2), pages 135-148, April.
    6. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lívia Mariana Lopes de Souza Torres & Francisco de Sousa Ramos, 2026. "Data envelopment analysis and game theory: Where are we? Where are we going?," Annals of Operations Research, Springer, vol. 358(2), pages 929-983, March.
    2. Yang Huang & Meiqiang Wang, 2024. "Efficiency evaluation of China’s high-tech industry with a dynamic network data envelopment analysis game cross-efficiency model," Operational Research, Springer, vol. 24(1), pages 1-36, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohammad Nemati & Reza Kazemi Matin & Mehdi Toloo, 2020. "A two-stage DEA model with partial impacts between inputs and outputs: application in refinery industries," Annals of Operations Research, Springer, vol. 295(1), pages 285-312, December.
    2. Sotiros, Dimitris & Koronakos, Gregory & Despotis, Dimitris K., 2019. "Dominance at the divisional efficiencies level in network DEA: The case of two-stage processes," Omega, Elsevier, vol. 85(C), pages 144-155.
    3. Bao-Ngoc Tong & Cheng-Ping Cheng & Lien-Wen Liang & Yi-Jun Liu, 2023. "Using Network DEA to Explore the Effect of Mobile Payment on Taiwanese Bank Efficiency," Sustainability, MDPI, vol. 15(8), pages 1-18, April.
    4. Fenfen Li & Bo Dai & Qifan Wu, 2021. "Dynamic Green Growth Assessment of China’s Industrial System with an Improved SBM Model and Global Malmquist Index," Mathematics, MDPI, vol. 9(20), pages 1-26, October.
    5. Liu, Hui-hui & Yang, Guo-liang & Liu, Xiao-xiao & Song, Yao-yao, 2020. "R&D performance assessment of industrial enterprises in China: A two-stage DEA approach," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    6. Amirali Fathi & Reza Farzipoor Saen, 2024. "Sustainability evaluation of transportation supply chains by common set of weights-network DEA and Shannon’s entropy in the presence of zero inputs," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 26(3), pages 7999-8025, March.
    7. Yande Gong & Joe Zhu & Ya Chen & Wade D. Cook, 2018. "DEA as a tool for auditing: application to Chinese manufacturing industry with parallel network structures," Annals of Operations Research, Springer, vol. 263(1), pages 247-269, April.
    8. Matthias Klumpp & Dominic Loske, 2021. "Sustainability and Resilience Revisited: Impact of Information Technology Disruptions on Empirical Retail Logistics Efficiency," Sustainability, MDPI, vol. 13(10), pages 1-20, May.
    9. Phung, Manh-Trung & Cheng, Cheng-Ping & Guo, Chuanyin & Kao, Chen-Yu, 2020. "Mixed Network DEA with Shared Resources: A Case of Measuring Performance for Banking Industry," Operations Research Perspectives, Elsevier, vol. 7(C).
    10. Dariush Khezrimotlagh & Sepideh Kaffash, 2025. "Navigating Efficiency: Insights from One-Stage and Two-Stage DEA Modeling in the Airline Industry," Annals of Operations Research, Springer, vol. 351(2), pages 1451-1487, August.
    11. Guccio, Calogero & Martorana, Marco & Mazza, Isidoro & Pignataro, Giacomo & Rizzo, Ilde, 2020. "An assessment of the performance of Italian public historical archives: Preservation vs utilisation," Journal of Policy Modeling, Elsevier, vol. 42(6), pages 1270-1286.
    12. Weiwei Zhu & Qian Zhang & Haiqing Wang, 2019. "Fixed costs and shared resources allocation in two-stage network DEA," Annals of Operations Research, Springer, vol. 278(1), pages 177-194, July.
    13. Fukuyama, Hirofumi & Weber, William L., 2010. "A slacks-based inefficiency measure for a two-stage system with bad outputs," Omega, Elsevier, vol. 38(5), pages 398-409, October.
    14. Saen, Reza Farzipoor & Karimi, Balal & Fathi, Amirali, 2025. "Unleashing efficiency potential: The power of non-convex double frontiers in sustainable transportation supply chains," Socio-Economic Planning Sciences, Elsevier, vol. 98(C).
    15. Shih-Heng Yu & Ming Chen & Fu-Chiang Yang, 2025. "Corporate social responsibility, profitability and marketability in business performance evaluation: a directional network slacks-based measure approach," Annals of Operations Research, Springer, vol. 353(3), pages 1211-1237, October.
    16. Peykani, Pejman & Seyed Esmaeili, Fatemeh Sadat & Pishvaee, Mir Saman & Rostamy-Malkhalifeh, Mohsen & Hosseinzadeh Lotfi, Farhad, 2024. "Matrix-based network data envelopment analysis: A common set of weights approach," Socio-Economic Planning Sciences, Elsevier, vol. 95(C).
    17. Chen, Yao & Cook, Wade D. & Zhu, Joe, 2010. "Deriving the DEA frontier for two-stage processes," European Journal of Operational Research, Elsevier, vol. 202(1), pages 138-142, April.
    18. Chiang Kao & Shiang-Tai Liu, 2022. "Stochastic efficiencies of network production systems with correlated stochastic data: the case of Taiwanese commercial banks," Annals of Operations Research, Springer, vol. 315(2), pages 1151-1174, August.
    19. Huang, Chin-wei & Ho, Foo Nin & Chiu, Yung-ho, 2014. "Measurement of tourist hotels׳ productive efficiency, occupancy, and catering service effectiveness using a modified two-stage DEA model in Taiwan," Omega, Elsevier, vol. 48(C), pages 49-59.
    20. Calogero Guccio & Anna Mignosa & Ilde Rizzo, 2017. "Disentangle inefficiency in the production activities of Italian national libraries: A network DEA approach," ACEI Working Paper Series AWP-04-2017, Association for Cultural Economics International, revised Mar 2017.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:747596. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.