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Cooperation and Competition Strategy Analysis of Decision-Making Units Based on Efficiency Game

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Abstract

Data envelopment analysis (DEA) method based on game theory effectively ranks the decision-making units (DMUs) by the view of cooperation or competition. The DEA method based on partial ordered set theory depicts the relationships among DMUs. However, these methods are unable to reveal the complex cooperation and competition relationships among DMUs. In this paper, an optimal model for DMUgroup game strategy isproposed based onthegeneralized DEA method and gametheory. According to this model, we can effectively depict the efficiency change of DMUs. Moreover, the effect of various game relationships on individual and the union of DMUs can be characterized. It is of positive significance for decision makers to find partners and moderate the cooperation and competition situation of their competitors. Finally, the cooperation and competition relationships of 9 express enterprises in a certain area in China are analyzed by using the method proposed in this paper.

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References

  • Almeida C R F, Li W, Meinerz G V, Li L (2016). Satis-ficing game approach to collaborative decision-making including airport management. IEEE Transactions on Intelligent Transportation Systems 17(8):2262–2271.

    Google Scholar 

  • Andersen P, Petersen N C (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science 39(10):1261–1264.

    MATH  Google Scholar 

  • Banker R D (1980). A game theoretic approach to measuring efficiency. European Journal of Operational Research 5(4):262–266.

    MathSciNet  MATH  Google Scholar 

  • Banker R D, Charnes A, Cooper W W (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30(9):1078–1092.

    MATH  Google Scholar 

  • Banker R D, Charnes A, Clarke R, Cooper W W (1989). Constrained game formulations and interpretations for data envelopment analysis. European Journal of Operational Research 40(3): 299-308.

    Google Scholar 

  • Cao L, Ma Z, Gao F, Ma S (2017). Analysisofeconomic benefit of the western provinces and cities in China based on generalized DEA method. Mathematics in Practice and Theory 47(3):64–73.

    Google Scholar 

  • Charnes A, Cooper W W, Rhodes E (1978). Measuring the efficiency of decision-making units. European Journal of Operational Research 2(6):429–444.

    MathSciNet  MATH  Google Scholar 

  • Chen Y, Liang L, Yang F (2006). A DEA game model approach to supply chain efficiency. Annals of Operations Research 145(1):5–13.

    MathSciNet  MATH  Google Scholar 

  • Chen Y, Zhu J (2004). Measuring information technology's indirect impact on firm performance. Information Technology and Management 5(1-2):9–22.

    Google Scholar 

  • Cheng Y, Yao L, He H, Mei S (2018).Anevaluation method for DEA game efficiency considering cross-competition game of DMUs. Control and Decision 33(9):1677–1685.

    MATH  Google Scholar 

  • Costa E F, Meza L A, Roboredo M C (2018). A DEA model to evaluate Brazilian container terminals. RAIRO - Operations Research 52(3):743–754.

    MathSciNet  MATH  Google Scholar 

  • Clarke R L (1988). A study of the effects for repeated applications of data envelopment analysis of efficiency of air for vehicle maintenance units in the Tactical Air Command and a test for the presence of organizational slack using Rajiv Banker' s game theory formulations. PhD, The University of Texas at Austin.

    Google Scholar 

  • Emrouznejad A, Yang G L (2018). A survey and analysis of the first 40 years of scholarly literature in DEA: 1978-2016. Socio-Economic Planning Sciences 61(1):4–8.

    Google Scholar 

  • Fare R, Grosskopf S (1985). A nonparametric cost approach to scale efficiency. The Scandinavian Journal of Economics 87(4):594–604.

    MATH  Google Scholar 

  • Golany B, Rousseau JJ (1992). Efficiency evaluation games. In: Phillips and Rousseau J.J. (eds). Systems and Management Science by Extremal Methods. Kluwer Academic Press, Boston, UK.

    Google Scholar 

  • Hao G, Wei Q, Yan H (2000). The generalized DEA model and the convex cone constrained game. European Journal of Operational Research 126(3):515–525.

    MathSciNet  MATH  Google Scholar 

  • Li F, Zhu Q, Liang L (2018). Allocating a fixed cost based on a DEA-game cross efficiency approach. Expert Systems with Applications 96:196–207.

    Google Scholar 

  • Liang L, Cook W D, Zhu J (2008a). DEA models for two-stage processes: Game approach and efficiency decomposition. Naval Research Logistics 55(7):643–653.

    MathSciNet  MATH  Google Scholar 

  • Liang L, Wu J (2013). A retrospective and perspective view on cross efficiency of data envelopment analysis (DEA).Journal of University of Science and Technology of China 43(11):941–947.

    Google Scholar 

  • Liang L, Wu J, Cook W D, Zhu J (2008b). The DEA game cross-efficiency model and its Nash equilibrium. Operations Research 56(5):1278–1288.

    MathSciNet  MATH  Google Scholar 

  • Liu W, Wang Y, Lu S (2018). Rankingdecision-makingunits based oncross-efficiency and cooperative game. Chinese Journal of Management Science 26(4):163–170

    Google Scholar 

  • Ma C, Liu D, Zhou Z, Zhao W, Liu W (2014). Game cross efficiency for systems with two-stage structures. Journal of Applied Mathematics 2014(9):1–8.

    MathSciNet  MATH  Google Scholar 

  • Ma R, Yao L, Jin M, Ren P (2014). The DEA game cross-efficiency model for supplier selection problem under competition. Applied Mathematics and Information Sciences 8(2):811–818.

    Google Scholar 

  • Ma S, Ma Z (2014). Generalized data envelopment analysis method based on C2W model. Systems Engineering-Theory and Practice 34(4):899–909.

    Google Scholar 

  • Ma Z, Ma S (2011). Generalized data envelopment analysis method based on C2WY model. Systems Engineering 26(2):251–261.

    Google Scholar 

  • Ma Z (2002). An evaluation method based on some sample units. Journal of Inner Mongolia University (Natural Science Edition) 33(6):606–610.

    Google Scholar 

  • Ma Z (2003). Frontier that formed by some sample units and its applying. Systems Engineering - Theory and Practice 23(12):32–37.

    Google Scholar 

  • Ma Z (2012). DEA model with generalized reference set and its properties. Systems Engineering and Electronics 34(4):709–714.

    Google Scholar 

  • Ma Z, Cao L, Bao S (2018). A resource optimized allocation method of multi-level complex system. Systems Engineering Theory and Practice 38(7):1802–1818.

    Google Scholar 

  • Ma Z, Tang H, Dai Y (2002). Using theory of partially ordered sets to study data envelopment analysis. Journal of Systems Engineering 17(1):19–25.

    Google Scholar 

  • Ma Z, Zhao C (2016). Measure method for efficiency of generalized DEA. Systems Engineering and Electronics 38(11):2572–2585.

    Google Scholar 

  • Muren, Ma Z, Cui W (2013). Data envelopment analysis method based on poset theory. Systems Engineering and Electronics 36(9):1782–1787.

    Google Scholar 

  • Muren, Ma Z, Cui W (2012). Fuzzy data envelopment analysis approach based on sample decision making units. Systems Engineering and Electronics 23(3):399–407.

    Google Scholar 

  • Nakabayashi K, Tone K (2006). Egoist's dilemma: a DEA game. (data envelopment analysis). Omega: The International Journal of Management Science 34(2):135–148.

    Google Scholar 

  • Rezaee M J, Moini A, Makui A (2012). Operational and non-operational performance evaluation of thermal power plants in Iran: A game theory approach. Energy 38(1):96–103.

    Google Scholar 

  • Rezaee M J, Izadbakhsh H, Yousefi S (2016). An improvement approach based on DEA-game theory for comparison of operational and spatial efficiencies in urban transportation systems. KSCE Journal of Civil Engineering 20(4):1526–1531.

    Google Scholar 

  • Rezaee M J, Shokry M (2017). Game theory versus multi-objective model for evaluating multi-level structure by using data envelopment analysis. International Journal of Management Science and Engineering Management 12(4):245–255.

    Google Scholar 

  • Sadjadi S J, Bayati M F (2016). Two-Tier supplier base efficiency evaluation via network DEA: A game theory approach. International Journal of Engineering, Transactions A: Basics 29(7):931–939.

    Google Scholar 

  • Seiford L M, Thrall R M (1990). Recent developments in DEA:themathematicalprogrammingapproachtofron-tier analysis. Journal of Econometrics 46(1-2):7–38.

    Google Scholar 

  • Semple J H, Rousseau J J (1995). Two-personratio efficiency games. Management Science 41(3): 435–441.

    MATH  Google Scholar 

  • Sengupta J K (1990). Transformations in stochastic DEA models. Journal of Econometrics 46(1): 109–123.

    MathSciNet  MATH  Google Scholar 

  • Sexton T R, Silkman R H, Hogan A J (1986). Data envelopment analysis: Critique and extensions. New Directions for Program Evaluation 1986(32):73–105.

    Google Scholar 

  • Sohraiee S, Lotfi F H (2010). A satisficing game theory approach for efficiency evaluation with interval data. Applied Mathematical Sciences 4(25-28):1337–1353.

    MATH  Google Scholar 

  • Sun N, Ma S, Ma Z (2015). Research on efficiency of generalized fuzzy DEA. Mathematics in Practice and Theory 45(3):181–186.

    Google Scholar 

  • Tchangani A P (2006). A satisficing game theory approach for group evaluation of production units. Decision Support Systems 42(2):778–788.

    Google Scholar 

  • Wang M, Li Y (2014). Supplier evaluation based on Nash bargaining game model. Expert Systems with Applications 41(9):4181–4185.

    Google Scholar 

  • Wu H, Liang L, Wu J, Yang F (2010). Analysis and develop-mentofDEA game model. Chinese Journal of Management Science 18(05):184–192.

    Google Scholar 

  • Wu J, Liang L (2012). A multiple criteria ranking method based on game cross-evaluation approach. Annals of Operations Research 197(1):191–200.

    MathSciNet  MATH  Google Scholar 

  • Wu J, Liang L, Yang F (2009a). Determinationofthe weights for the ultimate cross efficiency using Shapley value in cooperative game. Expert Systems with Applications 36(1):872–876.

    Google Scholar 

  • Wu J, Liang L, Chen Y (2009b). DEA game cross-efficiency approach to Olympic rankings. Omega 37(4):909–918.

    Google Scholar 

  • Yi R, Ma Z (2019). A generalized sample interval DEA model with only output. Chinese Journal of Management Science 27(1):194–204.

    Google Scholar 

  • Zhang W, Wang X, Qi T (2018). Transmission cost allocation based on data envelopment analysis and cooperative game method. Electric Power Components and Systems 46(2):208–217.

    Google Scholar 

  • Zuo K, Guan J (2017). Measuring the R&D efficiency of regions by a parallel DEA game model. Scientometrics 112(1):175–194.

    Google Scholar 

Download references

Acknowledgments

We would like to thank referees for their help to improve the quality of the paper. The research is supported by National Natural Science Funds of China under Grant Nos. 70821001, 71661025 and 71401084, and Inner Mongolia Natural Science Foundation under Grant Nos. 2016MS0705, 2017JQ02 and 2019MS07008, Inner Mongolia Grassland Talent Project under Grant No. 12000-12102012, China Post-Doctoral Fund under Grant No. 2018M631323, Project of Inner Mongolia Institute of Data Science and Big Data under Grant No. BDY18007, Inner Mogolia Medical University Excellext Teacher Preject under Grant No. NYJTXX201915.

Author information

Authors and Affiliations

  1. School of Mathematics Science, Inner Mongolia University, Hohhot, 010021, China

    Li Cao

  2. College of Computer and Information, Inner Mongolia Medical University, Hohhot, 010051, China

    Li Cao

  3. School of Economics and Management, Inner Mongolia University, Hohhot, 010021, China

    Zhanxin Ma

  4. Key Laboratory of Rail Transit, Beijing Jiaotong University, Beijing, 100044, China

    Muren

  5. School of Economics and Management, Inner Mongolia University of Technology, Hohhot, 010110, China

    Muren

Authors
  1. Li Cao
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  2. Zhanxin Ma
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Corresponding authors

Correspondence to Zhanxin Ma or Muren.

Additional information

Li CAO is associate professor in College of Computer and Information, Inner Mongolia Medical University. He received his doctorate from Inner Mongolia University in July 2019. His research interests focus on allocation of data envelopment analysis (DEA), game theory, decision analysis. He has articles published in peer-reviewed journals, such as Systems Engineering-Theory & Practice, Mathematics in Practice and Theory, and others.

Zhanxin Ma is a professor in School of Economics and Management, Inner Mongolia University. His areas of specialty include decision analysis and data envelopment analysis. Hehas published more than 100 articlesin a wide range of academic and professional journals, including Systems Engineering and Electronics (SCI), Applied Soft Computing Journal (SCI), Systems Engineering-Theory & Practice, Systems Engineering, Journal of Systems Engineering, Control and Decision, Operations Research Transactions, Chinese Journal of Management Science, Fuzzy Systems and Mathematics, Journal of Traffic and Transportation Engineering, Chinese Journal of Management and others.

Muren isaprofessor inSchoolof Economics and Management, Inner Mongolia University of Technology. His areas of specialty include mathematical modeling and data envelopment analysis. He has published more than 20 articles in a wide range of academic and professional journals, including Systems Engineering and Electronics (SCI), Applied Soft Computing Journal (SCI), Control and Decision, Systems Engineering and Electronics, Fuzzy Systems and Mathematics, Chinese Journal of Management Science, and others.

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Cao, L., Ma, Z. & Muren Cooperation and Competition Strategy Analysis of Decision-Making Units Based on Efficiency Game. J. Syst. Sci. Syst. Eng. 29, 235–248 (2020). https://doi.org/10.1007/s11518-019-5417-9

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