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A game theoretical model of DEA efficiency

Author

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  • G Hao

    (City University of Hong Kong)

  • Q L Wei

    (Renmin University of China)

  • H Yan

    (The Hong Kong Polytechnic University)

Abstract

Motivated by the inherent competitive nature of the DEA efficiency assessment process, some effort has been made to relate DEA models to game theory. Game theory is considered not only a more natural source of representing competitive situations, but also beneficial in revealing additional insights into practical efficiency analysis. Past studies are limited to connecting efficiency games to some particular versions of DEA models. The generalised DEA model considered in this study unifies various important DEA models and presents a basic formulation for the DEA family. By introducing a generalised convex cone constrained efficiency game model in assembling the generalised DEA model, a rigorous connection between game theory and the DEA family is established. We prove the existence of optimal strategies in the generalised efficiency game. We show the equivalence between game efficiency and DEA efficiency. We also provide convex programming models for determination of the optimal strategies of the proposed games, and show that the game efficiency unit corresponds to the non-dominated solution in its corresponding multi-objective programming problem. Our study largely extends the latest developments in this area. The significance of such an extension is for research and applications of both game theory and DEA.

Suggested Citation

  • G Hao & Q L Wei & H Yan, 2000. "A game theoretical model of DEA efficiency," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(11), pages 1319-1329, November.
    • Handle: RePEc:pal:jorsoc:v:51:y:2000:i:11:d:10.1057_palgrave.jors.2601006
    DOI: 10.1057/palgrave.jors.2601006
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    Citations

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    Cited by:

    1. Gattoufi, Said & Oral, Muhittin & Kumar, Ashok & Reisman, Arnold, 2004. "Epistemology of data envelopment analysis and comparison with other fields of OR/MS for relevance to applications," Socio-Economic Planning Sciences, Elsevier, vol. 38(2-3), pages 123-140.
    2. Lozano, S., 2013. "DEA production games," European Journal of Operational Research, Elsevier, vol. 231(2), pages 405-413.
    3. Sickles, Robin C. & Song, Wonho & Zelenyuk, Valentin, 2018. "Econometric Analysis of Productivity: Theory and Implementation in R," Working Papers 18-008, Rice University, Department of Economics.
    4. Valentin Zelenyuk, 2018. "Some Mathematical and Historical Clarifications on Aggregation in Efficiency and Productivity Analysis and Connection to Economic Theory," CEPA Working Papers Series WP032018, School of Economics, University of Queensland, Australia.
    5. Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.
    6. 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.
    7. Gattoufi, Said & Oral, Muhittin & Reisman, Arnold, 2004. "A taxonomy for data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 38(2-3), pages 141-158.

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