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Information sharing in DEA: A cooperative game theory approach

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  • Lozano, S.

Abstract

In this paper, a cooperative DEA game is proposed based on the idea that different organizations can gain if they share data on the input consumption and output production of their processing units. A larger data sample allows a more complete description of the Production Possibility Set and, consequently, of the efficient frontier. However, since not all organizations will benefit in the same way, it is convenient to use cooperative game theory in order to share the benefits of the cooperation. The proposed cooperative DEA game is shown to be subadditive and balanced. Models for computing the τ-value of the game and checking its stability, taking into account the exponential number of coalitions that exist when the number of organizations is large, are also presented. The approach is illustrated with a dataset from the literature.

Suggested Citation

  • Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:3:p:558-565
    DOI: 10.1016/j.ejor.2012.05.014
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    1. Banker, Rajiv D., 1980. "A game theoretic approach to measuring efficiency," European Journal of Operational Research, Elsevier, vol. 5(4), pages 262-266, October.
    2. Du, Juan & Liang, Liang & Chen, Yao & Cook, Wade D. & Zhu, Joe, 2011. "A bargaining game model for measuring performance of two-stage network structures," European Journal of Operational Research, Elsevier, vol. 210(2), pages 390-397, April.
    3. Hallefjord, Asa & Helming, Reidun & Jornsten, Kurt, 1995. "Computing the Nucleolus When the Characteristic Function Is Given Implicitly: A Constraint Generation Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 357-372.
    4. Cook, Wade D. & Kress, Moshe, 1999. "Characterizing an equitable allocation of shared costs: A DEA approach," European Journal of Operational Research, Elsevier, vol. 119(3), pages 652-661, December.
    5. J. J. Rousseau & J. H. Semple, 1995. "Two-Person Ratio Efficiency Games," Management Science, INFORMS, vol. 41(3), pages 435-441, March.
    6. Beasley, J. E., 2003. "Allocating fixed costs and resources via data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 147(1), pages 198-216, May.
    7. Banker, R. D. & Charnes, A. & Cooper, W. W. & Clarke, R., 1989. "Constrained game formulations and interpretations for data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 40(3), pages 299-308, June.
    8. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. 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.
    10. S Lozano & G Villa, 2010. "DEA-based pre-merger planning tool," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(10), pages 1485-1497, October.
    11. Zha, Yong & Liang, Liang, 2010. "Two-stage cooperation model with input freely distributed among the stages," European Journal of Operational Research, Elsevier, vol. 205(2), pages 332-338, September.
    12. Tijs, S.H. & Driessen, T.S.H., 1986. "Game theory and cost allocation problems," Other publications TiSEM 376c24c5-c95d-4d29-96b6-4, Tilburg University, School of Economics and Management.
    13. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    14. S. H. Tijs & T. S. H. Driessen, 1986. "Game Theory and Cost Allocation Problems," Management Science, INFORMS, vol. 32(8), pages 1015-1028, August.
    15. Li, Yongjun & Yang, Feng & Liang, Liang & Hua, Zhongsheng, 2009. "Allocating the fixed cost as a complement of other cost inputs: A DEA approach," European Journal of Operational Research, Elsevier, vol. 197(1), pages 389-401, August.
    16. Zhu, Joe, 2004. "A buyer-seller game model for selection and negotiation of purchasing bids: Extensions and new models," European Journal of Operational Research, Elsevier, vol. 154(1), pages 150-156, April.
    17. K Tone, 2002. "A strange case of the cost and allocative efficiencies in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1225-1231, November.
    18. 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.
    19. Nakabayashi, Ken & Tone, Kaoru, 2006. "Egoist's dilemma: a DEA game," Omega, Elsevier, vol. 34(2), pages 135-148, April.
    20. Wu, Jie & Liang, Liang & Chen, Yao, 2009. "DEA game cross-efficiency approach to Olympic rankings," Omega, Elsevier, vol. 37(4), pages 909-918, August.
    21. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
    22. 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.
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