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DEA game cross-efficiency approach to Olympic rankings

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  • Wu, Jie
  • Liang, Liang
  • Chen, Yao
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    Abstract

    A number of studies have used data envelopment analysis (DEA) to evaluate the performance of the countries in Olympic games. While competition exists among the countries in Olympic games/rankings, all these DEA studies do not model competition among peer decision making units (DMUs) or countries. These DEA studies find a set of weights/multipliers that keep the efficiency scores of all DMUs at or below unity. Although cross efficiency goes a further step by providing an efficiency measure in terms of the best multiplier bundle for the unit and all the other DMUs, it is not always unique. This paper presents a new and modified DEA game cross-efficiency model where each DMU is viewed as a competitor via non-cooperative game. For each competing DMU, a multiplier bundle is determined that optimizes the efficiency score for that DMU, with the additional constraint that the resulting score should be at or above that DMU 's estimated best performance. The problem, of course, arises that we will not know this best performance score for the DMU under evaluation until the best performances of all other DMUs are known. To combat this "chicken and egg" phenomenon, an iterative approach leading to the Nash equilibrium is presented. The current paper provides a modified variable returns to scale (VRS) model that yields non-negative cross-efficiency scores. The approach is applied to the last six Summer Olympic Games. Our results may indicate that our game cross-efficiency model implicitly incorporates the relative importance of gold, silver and bronze medals without the need for specifying the exact assurance regions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 37 (2009)
    Issue (Month): 4 (August)
    Pages: 909-918

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    Handle: RePEc:eee:jomega:v:37:y:2009:i:4:p:909-918

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    Keywords: Data envelopment analysis (DEA) Cross efficiency Olympic Game Nash equilibrium;

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    Cited by:
    1. Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.
    2. Yang, Guo-liang & Yang, Jian-bo & Liu, Wen-bin & Li, Xiao-xuan, 2013. "Cross-efficiency aggregation in DEA models using the evidential-reasoning approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 393-404.
    3. Chen, Yao & Du, Juan & Huo, Jiazhen, 2013. "Super-efficiency based on a modified directional distance function," Omega, Elsevier, vol. 41(3), pages 621-625.
    4. Li, Yongjun & Yang, Min & Chen, Ya & Dai, Qianzhi & Liang, Liang, 2013. "Allocating a fixed cost based on data envelopment analysis and satisfaction degree," Omega, Elsevier, vol. 41(1), pages 55-60.
    5. Sitarz, Sebastian, 2012. "Mean value and volume-based sensitivity analysis for Olympic rankings," European Journal of Operational Research, Elsevier, vol. 216(1), pages 232-238.
    6. Rödder, W. & Reucher, E., 2012. "Advanced X-efficiencies for CCR- and BCC-models – towards Peer-based DEA controlling," European Journal of Operational Research, Elsevier, vol. 219(2), pages 467-476.
    7. Demirbag, Mehmet & Tatoglu, Ekrem & Glaister, Keith W. & Zaim, Selim, 2010. "Measuring strategic decision making efficiency in different country contexts: A comparison of British and Turkish firms," Omega, Elsevier, vol. 38(1-2), pages 95-104, February.
    8. Lozano, S., 2013. "DEA production games," European Journal of Operational Research, Elsevier, vol. 231(2), pages 405-413.
    9. Assaf, A. George & Barros, Carlos & Sellers-Rubio, Ricardo, 2011. "Efficiency determinants in retail stores: a Bayesian framework," Omega, Elsevier, vol. 39(3), pages 283-292, June.
    10. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
    11. Partovi, Fariborz Y., 2011. "Corporate philanthropic selection using data envelopment analysis," Omega, Elsevier, vol. 39(5), pages 522-527, October.
    12. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2011. "Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation," Omega, Elsevier, vol. 39(6), pages 634-641, December.
    13. Wang, Ying-Ming & Chin, Kwai-Sang, 2011. "The use of OWA operator weights for cross-efficiency aggregation," Omega, Elsevier, vol. 39(5), pages 493-503, October.
    14. Soares de Mello, João Carlos C.B. & Angulo Meza, Lidia & da Silveira, Juliana Quintanilha & Gomes, Eliane Gonçalves, 2013. "About negative efficiencies in Cross Evaluation BCC input oriented models," European Journal of Operational Research, Elsevier, vol. 229(3), pages 732-737.
    15. Soltanifar, Mehdi & Shahghobadi, Saeid, 2013. "Selecting a benevolent secondary goal model in data envelopment analysis cross-efficiency evaluation by a voting model," Socio-Economic Planning Sciences, Elsevier, vol. 47(1), pages 65-74.

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