Skip to main content
SpringerLink
Log in

DEA and Cooperative Game Theory

  • Chapter
  • First Online:
Handbook of Operations Analytics Using Data Envelopment Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 239))

Abstract

In this chapter the possibilities of hybridizing data envelopment analysis (DEA) and cooperative games are studied. Specifically, bargaining games and transferable utility games (TU games) are considered. There are already a number of different DEA approaches that are based on these types of cooperative games but, more importantly, there is the potential for further cooperation from both techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    When the solution recommends a singleton we will refer to it as an allocation rule.

  2. 2.

    The restriction of (N, v) to the coalition S is the TU-game (S, v S ), where, for each T ⊂ S, v S (T): = v(T).

References

  • Aparicio, J., Borras, F., Pastor, J. T., & Vidal, F. (2013). Accounting for slacks to measure and decompose revenue efficiency in the Spanish designation of origin wines with DEA. European Journal of Operational Research, 231, 443–451.

    Article  Google Scholar 

  • Aubin, J. P. (1981). Cooperative fuzzy games. Mathematics of Operations Research, 6, 1–13.

    Article  Google Scholar 

  • Aumann, R. J., & Maschler, M. (1964). The bargaining set for cooperative games. In M. Dresher, L. S. Shapley, & A. Tucker (Eds.), Advances in game theory (Vol. 52, pp. 443–476). Princeton: Princeton University Press.

    Google Scholar 

  • Bondareva, O. (1963). Some applications of linear programming methods to the theory of cooperative games. Problemy Kybernetiki, 10, 119–139.

    Google Scholar 

  • Borrero, D.V., Hinojosa, M.A., & Mármol, A.M. (2016). DEA production games and Owen allocations. European Journal of Operational Research, 252, 921–930.

    Google Scholar 

  • Chen, Y., Cook, W.D., Li, N., & Zhu, J. (2009). Additive efficiency decomposition in two-stage DEA. European Journal of Operational Research, 196, 1170–1176.

    Article  Google Scholar 

  • Conley, J.P., & Wilkie, S. (1991). Bargaining theory without convexity. Economics Letters, 36, 365–369.

    Article  Google Scholar 

  • Conley, J.P., & Wilkie, S. (1996). An extension of the Nash bargaining solution to non-convex problems. Games and Economic Behaviour, 13, 26–38.

    Article  Google Scholar 

  • Cook, W.D., Liang, L., & Zhu, J. (2010). Measuring performance of two-stage network structures by DEA: A review and future perspective. Omega, 38, 423–430.

    Article  Google Scholar 

  • Curiel, I.J. (1997). Cooperative game theory and applications. Dordrecht: Kluwer Academic Publisher.

    Book  Google Scholar 

  • Du, J., Liang, L., Chen, Y., Cook, W.D., & Zhu, J. (2011). A bargaining game model for measuring performance of two stage network structures. European Journal of Operational Research, 210, 390–397.

    Article  Google Scholar 

  • Emrouznejad, A., Tavana, M., & Hatami-Marbini, A. (2014). The state of the art in fuzzy data envelopment analysis. Performance Measurement with Fuzzy Data Envelopment Analysis, 309, 1–45.

    Article  Google Scholar 

  • Färe, R., & Grosskopf, S. (1996). Productivity and intermediate products: A frontier approach. Economics Letters, 50, 65–70.

    Article  Google Scholar 

  • Fukuyama, H., & Weber, W.L. (2010). A slacks-based inefficiency measure for a two-stage system with bad outputs. Omega, 38(5), 398–409.

    Article  Google Scholar 

  • Gillies, D.B. (1953). Some theorems on n-person games. Ph.D. Thesis, Princeton.

    Google Scholar 

  • González, A., & Vila, M.A. (1992). Dominance relation on fuzzy numbers. Information Sciences, 64, 1–16.

    Article  Google Scholar 

  • Green, R., Doyle, J., & Cook, W.D. (1996). Preference voting and project ranking using DEA and cross-evaluation. European Journal of Operational Research, 90, 461–472.

    Article  Google Scholar 

  • Halkos, G.E., Tzeremes, N.G., & Kourtzidis, S.A. (2014). A unified classification of two-stage DEA models. Surveys in Operations Research and Management Science, 19, 1–16.

    Article  Google Scholar 

  • Hatami-Marbini, A., Emrouznejad, A., & Tavana, M. (2011). A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making. European Journal of Operational Research, 214, 457–472.

    Article  Google Scholar 

  • Herrero, M.J. (1989) Nash program: non-convex bargaining problems. Journal of Economic Theory, 49, 266–277.

    Article  Google Scholar 

  • Hinojosa, M.A., Lozano, S., & Mármol, A. (2015a). Nash decomposition for process efficiency in multistage production systems. Working paper submitted for publication.

    Google Scholar 

  • Hinojosa, M.A., Lozano, S., & Mármol, A. (2015b). DEA production games with fuzzy output prices. Working paper submitted for publication.

    Google Scholar 

  • Hinojosa, M.A., Mármol, A.M., Monroy, L., & Fernández, F.R. (2013). A multi-objective approach to fuzzy linear production games. International Journal of Information Technology and Decision Making, 12(5), 927–943.

    Article  Google Scholar 

  • Jahangoshai Rezaee, M., Moini, A., & Hali-Aji Asgari, F. (2012a). Unified performance evaluation of health centers with integrated model of data envelopment analysis. Journal of Medical Systems, 36, 3805–3815.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Jahanshahloo, G.R., Hosseinzadeh, L.F., & Sohraiee, S. (2006). Egoist’s dilemma with interval data. Applied Mathematics and Computation, 183, 94–105.

    Article  Google Scholar 

  • Jalali-Naini, S.G., Moini, A., & Jahangoshai Rezaee, M. (2013). Nash bargaining game model for two parallel stages process evaluation with shared inputs. International Journal of Advanced Manufacturing Technology, 67, 475–484.

    Article  Google Scholar 

  • Kalai, E., & Smorodinsky, M. (1975). Other solutions to Nash’s bargaining problem. Econometrica, 43, 513–518.

    Article  Google Scholar 

  • Kao, C. (2014). Network data envelopment analysis: A review. European Journal of Operational Research, 239, 1–16.

    Article  Google Scholar 

  • Kao, C., & Hwang, S.N. (2008). Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European Journal of Operational Research, 185, 418–429.

    Article  Google Scholar 

  • Kao, C., & Hwang, S.N. (2010). Efficiency measurement for network systems: IT impact on firm performance. Decision Support Systems, 48(3), 437–446.

    Google Scholar 

  • Kao, C., & Hwang, S.N. (2011). Decomposition of technical and scale efficiencies in two-stage production systems. European Journal of Operational Research, 211, 515–559.

    Article  Google Scholar 

  • Kao, C., & Hwang, S.N. (2014). Multi-period efficiency and Malmquist productivity index in two-stage production systems. European Journal of Operational Research, 232, 512–521.

    Article  Google Scholar 

  • Li, Y., & Liang, L. (2010). A Shapley value index on the importance of variables in DEA models. Expert Systems with Applications, 37, 6287–6292.

    Article  Google Scholar 

  • Li, S., & Zhang, Q. (2009). A simplified expression of the Shapley function for fuzzy games. European Journal of Operational Research, 196, 234–245.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lozano, S. (2012). Information sharing in DEA: A cooperative game theory approach. European Journal of Operational Research, 222, 558–565.

    Article  Google Scholar 

  • Lozano, S. (2013a). Using DEA to find the best partner for a horizontal cooperation. Computers & Industrial Engineering, 66, 286–292.

    Article  Google Scholar 

  • Lozano, S. (2013b). DEA production games. European Journal of Operational Research, 231, 405–413.

    Article  Google Scholar 

  • Lozano, S., Moreno, P., Adenso-Díaz, B., & Algaba, E. (2013). Cooperative game theory approach to allocating benefits of horizontal cooperation. European Journal of Operational Research, 229, 444–452.

    Article  Google Scholar 

  • Lozano, S., Hinojosa, M.A., & Mármol, A.M. (2014). Set-valued DEA production games. Omega, 52, 92–100.

    Article  Google Scholar 

  • Monroy, L., Hinojosa, M.A., Mármol, A.M., & Fernández, F.R. (2013). Set-valued cooperative games with fuzzy payoffs. The fuzzy assignment game. European Journal of Operational Research, 225(1), 85–90.

    Article  Google Scholar 

  • Nakabayashi, K., & Tone, K. (2006). Egoist’s dilemma: A DEA game. Omega, 34, 135–148.

    Article  Google Scholar 

  • Nakabayashi, K., Sahoo, B.K., & Tone, K. (2009). Fair allocation based on two criteria: A DEA game view of “Add them up and divide by two”. Journal of the Operations Research Society of Japan, 52(2), 131–146.

    Google Scholar 

  • Nash, J.F. (1950). The bargaining problem. Econometrica, 28, 155–162.

    Article  Google Scholar 

  • Nishizaki, I., & Sakawa, M. (2001). Fuzzy and multiobjective games for conflict resolution. Heidelberg: Physica-Verlag

    Book  Google Scholar 

  • Omrani, H., Gharizadeh Beiragh, R., & Shafiei Kaleibari, S. (2015). Performance assessment of Iranian electricity distribution companies by an integrated cooperative game data envelopment analysis principal component analysis approach. Electrical Power and Energy Systems, 64, 617–625.

    Article  Google Scholar 

  • Owen, G. (1975). On the core of linear production games. Mathematical Programming, 9, 358–370.

    Article  Google Scholar 

  • Ramík, J., & Římánek, J. (1985). Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets and Systems, 16(2), 123–138.

    Google Scholar 

  • Roth, A.E. (1979). An impossibility result concerning n-person bargaining games. International Journal of Game Theory, 8, 129–132.

    Article  Google Scholar 

  • Schmeidler, D. (1969). The nucleolus of a characteristic function game. SIAM Journal on Applied Mathematics, 17(6), 1163–1170.

    Article  Google Scholar 

  • Sekine, S., Fu, J., & Muto, S. (2014). Game theoretic approaches to weight assignments in data envelopment analysis problems. Mathematical Problems in Engineering. doi: 10.1155/2014/434252.

    Google Scholar 

  • Shapley, L.S. (1953). A value for n-person games. In H. Kuhn, & A. Tucker (Eds.), Contributions to the theory of games II. Annals of Mathematics Studies. Princeton: Princeton University Press.

    Google Scholar 

  • Shapley, L.S. (1967). On balanced sets and cores. Naval Research Logistics Quarterly, 14, 453–460.

    Article  Google Scholar 

  • Sugiyama, M., & Sueyoshi, T. (2014). Finding a common weight vector of data envelopment analysis based upon bargaining game. Studies in Engineering and Technology. doi:10.11114/set.v1i1.277.

    Google Scholar 

  • Thomson, W. (1980). Two characterizations of the Raiffa solution. Economics Letters, 6, 225–231.

    Article  Google Scholar 

  • Tijs, S.H. (1981). Bounds for the core and the τ-value. In: O. Moeschlin, & D. Pallaschke (Eds.), Game theory and mathematical economics (pp. 123–132). Amsterdam: North-Holland Publishing Company

    Google Scholar 

  • Tone, K. (2002). A strange case of the cost and allocative efficiencies in DEA. Journal of the Operational Research Society, 53, 1225–1231.

    Article  Google Scholar 

  • Tone, K., & Tsutsui, M. (2009). Network DEA: A slacks-based measure approach. European Journal of Operational Research, 197, 243–252.

    Article  Google Scholar 

  • Tone, K., & Tsutsui, M. (2014). Dynamic DEA with network structure: A slacks-based measure approach. Omega, 42, 124–131.

    Article  Google Scholar 

  • von Neumann, J., & Mongerstern, O. (1944). The theory of games and economics behaviour. Princeton: Princeton University Press.

    Google Scholar 

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

    Article  Google Scholar 

  • Weber, R.J. (1988). Probabilistic values for games. In The Shapley value (pp. 101–119). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Wu, H.C. (2012), Proper cores and dominance cores of fuzzy games. Fuzzy Optimization and Decision Making, 11(1), 47–72.

    Article  Google Scholar 

  • Wu, J., Liang, L., & Zha, Y.C. (2008). Determination of the weights of ultimate cross efficiency based on the solution of nucleolus in cooperative game. Systems Engineering-Theory and Practice, 28(5), 92–97.

    Article  Google Scholar 

  • Wu, J., Liang, L., Yang, F., & Yan, H. (2009a). Bargaining game model in the evaluation of decision making units. Expert Systems with Applications, 36, 4357–4362.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wu, H., Du, S., Liang, L., & Zhou, Y. (2013). A DEA-based approach for fair reduction and reallocation of emission permits. Mathematical and Computer Modelling, 58, 1095–1101.

    Article  Google Scholar 

  • Yang, X., & Morita, H. (2013) Efficiency improvement from multiple perspectives: An application to Japanese banking industry. Omega, 41(3), 501–509.

    Article  Google Scholar 

  • Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338–353.

    Article  Google Scholar 

  • Zhou, Z., Sun, L., Yang, W., Liu, W., & Ma, C. (2013). A bargaining game model for efficiency decomposition in the centralized model of two-stage systems. Computers and Industrial Engineering, 64, 103–108.

    Article  Google Scholar 

Download references

Acknowledgements

This research has been partially financed by the Spanish Ministry of Science and Innovation, projects, ECO2011-29801-C02-01 and ECO2011-29801-C02-02, and by the Consejería de Innovación de la Junta de Andalucía, project P11-SEJ-7782 and P10-TEP-6332.

Author information

Authors and Affiliations

  1. Sevilla University, Sevilla, Spain

    Sebastián Lozano & Amparo María Mármol

  2. Pablo de Olavide University, Sevilla, Spain

    Miguel Ángel Hinojosa & Diego Vicente Borrero

Authors
  1. Sebastián Lozano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miguel Ángel Hinojosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amparo María Mármol
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Diego Vicente Borrero
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel Ángel Hinojosa .

Editor information

Editors and Affiliations

  1. Dept of Business Administration, Ming Chuan University, Taipei, Taiwan

    Shiuh-Nan Hwang

  2. College of Maritime Science & Mgmt, National Taiwan Ocean University, Keelung, Taiwan

    Hsuan-Shih Lee

  3. School of Business, Worcester Polytechnic Institute, Worcester, Massachusetts, USA

    Joe Zhu

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this chapter

Cite this chapter

Lozano, S., Hinojosa, M.Á., Mármol, A.M., Borrero, D.V. (2016). DEA and Cooperative Game Theory. In: Hwang, SN., Lee, HS., Zhu, J. (eds) Handbook of Operations Analytics Using Data Envelopment Analysis. International Series in Operations Research & Management Science, vol 239. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7705-2_9

Download citation

Publish with us

Policies and ethics

Search

Navigation