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The DEA Game Cross-Efficiency Model and Its Nash Equilibrium


  • Liang Liang

    () (School of Business, University of Science and Technology of China, He Fei, An Hui Province, People's Republic of China 230026)

  • Jie Wu

    () (School of Business, University of Science and Technology of China, He Fei, An Hui Province, People's Republic of China 230026)

  • Wade D. Cook

    () (Schulich School of Business, York University, Toronto, Ontario, Canada M3J 1P3)

  • Joe Zhu

    () (Department of Management, Worcester Polytechnic Institute, Worcester, Massachusetts 01609)


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.

Suggested Citation

  • Liang Liang & Jie Wu & Wade D. Cook & Joe Zhu, 2008. "The DEA Game Cross-Efficiency Model and Its Nash Equilibrium," Operations Research, INFORMS, vol. 56(5), pages 1278-1288, October.
  • Handle: RePEc:inm:oropre:v:56:y:2008:i:5:p:1278-1288
    DOI: 10.1287/opre.1070.0487

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    References listed on IDEAS

    1. Timothy Anderson & Keith Hollingsworth & Lane Inman, 2002. "The Fixed Weighting Nature of A Cross-Evaluation Model," Journal of Productivity Analysis, Springer, vol. 17(3), pages 249-255, May.
    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. Green, Rodney H. & Doyle, John R. & Cook, Wade D., 1996. "Preference voting and project ranking using DEA and cross-evaluation," European Journal of Operational Research, Elsevier, vol. 90(3), pages 461-472, May.
    4. Wade D. Cook & Moshe Kress, 1990. "A Data Envelopment Model for Aggregating Preference Rankings," Management Science, INFORMS, vol. 36(11), pages 1302-1310, November.
    5. Robert Becker & Subir Chakrabarti, 2005. "Satisficing behavior, Brouwer’s Fixed Point Theorem and Nash Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 63-83, July.
    6. D K Despotis, 2002. "Improving the discriminating power of DEA: focus on globally efficient units," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(3), pages 314-323, March.
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