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Two-Person Ratio Efficiency Games

Author

Listed:
  • J. J. Rousseau

    (Center of Cybernetic Studies, CBA 5.202, The University of Texas at Austin, Austin, Texas 78712-1177)

  • J. H. Semple

    (Department of Information Systems and Management Sciences, The University of Texas at Arlington, Box 19437, Arlington, Texas 76019)

Abstract

This paper demonstrates that a class of two-person games with ratio payoff functions can be solved using equivalent primal-dual linear programming formulations. The game's solution contains specialized information which may be used to conduct the efficiency evaluation currently done by the CCR ratio model of Data Envelopment Analysis (DEA). Consequently a rigorous connection between DEA's CCR model and the theory of games is established. Interpretations of these new solutions are discussed in the context of current ongoing applications.

Suggested Citation

  • J. J. Rousseau & J. H. Semple, 1995. "Two-Person Ratio Efficiency Games," Management Science, INFORMS, vol. 41(3), pages 435-441, March.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:3:p:435-441
    DOI: 10.1287/mnsc.41.3.435
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    Citations

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    Cited by:

    1. Chen, Yao, 2005. "Measuring super-efficiency in DEA in the presence of infeasibility," European Journal of Operational Research, Elsevier, vol. 161(2), pages 545-551, March.
    2. Lozano, S., 2013. "DEA production games," European Journal of Operational Research, Elsevier, vol. 231(2), pages 405-413.
    3. Y-W Chen & M Larbani & Y-P Chang, 2009. "Multiobjective data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1556-1566, November.
    4. Yang, Feng & Wu, Desheng Dash & Liang, Liang & O'Neill, Liam, 2011. "Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 212(3), pages 560-569, August.
    5. Hao, Gang & Wei, Quanling & Yan, Hong, 2000. "The generalized DEA model and the convex cone constrained game," European Journal of Operational Research, Elsevier, vol. 126(3), pages 515-525, November.
    6. Reza Fallahnejad & Mohammad Reza Mozaffari & Peter Fernandes Wanke & Yong Tan, 2024. "Nash Bargaining Game Enhanced Global Malmquist Productivity Index for Cross-Productivity Index," Games, MDPI, vol. 15(1), pages 1-21, January.
    7. Yung-Ho Chiu & Yu-Chuan Chen & Xue-Jie Bai, 2011. "Efficiency and risk in Taiwan banking: SBM super-DEA estimation," Applied Economics, Taylor & Francis Journals, vol. 43(5), pages 587-602.
    8. Saranga, Haritha, 2009. "The Indian auto component industry - Estimation of operational efficiency and its determinants using DEA," European Journal of Operational Research, Elsevier, vol. 196(2), pages 707-718, July.
    9. C A K Lovell & A P B Rouse, 2003. "Equivalent standard DEA models to provide super-efficiency scores," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 101-108, January.
    10. Mei Xue & Patrick T. Harker, 2002. "Note: Ranking DMUs with Infeasible Super-Efficiency DEA Models," Management Science, INFORMS, vol. 48(5), pages 705-710, May.
    11. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    12. Kairui Zuo & Jiancheng Guan, 2017. "Measuring the R&D efficiency of regions by a parallel DEA game model," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(1), pages 175-194, July.
    13. I. Contreras & S. Lozano & M. A. Hinojosa, 2021. "A bargaining approach to determine common weights in DEA," Operational Research, Springer, vol. 21(3), pages 2181-2201, September.
    14. Cheng, Gang & Qian, Zhenhua & Zervopoulos, Panagiotis, 2011. "Overcoming the infeasibility of super-efficiency DEA model: a model with generalized orientation," MPRA Paper 31991, University Library of Munich, Germany.
    15. Semple, John, 1997. "Constrained games for evaluating organizational performance," European Journal of Operational Research, Elsevier, vol. 96(1), pages 103-112, January.
    16. W D Cook & L Liang & Y Zha & J Zhu, 2009. "A modified super-efficiency DEA model for infeasibility," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(2), pages 276-281, February.
    17. Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.
    18. S Gattoufi & M Oral & A Kumar & A Reisman, 2004. "Content analysis of data envelopment analysis literature and its comparison with that of other OR/MS fields," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 911-935, September.
    19. Chen, Yao & Sherman, H. David, 2004. "The benefits of non-radial vs. radial super-efficiency DEA: an application to burden-sharing amongst NATO member nations," Socio-Economic Planning Sciences, Elsevier, vol. 38(4), pages 307-320, December.
    20. Jingjing Ding & Chenpeng Feng & Gongbing Bi & Liang Liang & M. Khan, 2015. "Cone ratio models with shared resources and nontransparent allocation parameters in network DEA," Journal of Productivity Analysis, Springer, vol. 44(2), pages 137-155, October.

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