Nothing Special   »   [go: up one dir, main page]
Skip to main content
SpringerLink
Log in

Optimization Implementation and Characterization of the Equal Allocation of Nonseparable Costs Value

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper devotes to the study of the equal allocation of nonseparable costs value for cooperative games. On the one hand, we show that the equal allocation of nonseparable costs value is the unique optimal solution that minimizes the total complaints for individual players over the pre-imputation set. On the other hand, analogously to the way of determining the Nucleolus, we obtain the equal allocation of nonseparable costs value by applying the lexicographic order over the individual complaints. Moreover, we offer alternative characterizations of the equal allocation of nonseparable costs value by proposing several new properties such as dual nullifying player property, dual dummifying player property and grand marginal contribution monotonicity.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Schmeidler, D.: The nucleolus of a characteristic function game. SIAM J. Appl. Math. 17, 517–520 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ruiz, L.M., Valenciano, F., Zarzuelo, J.M.: The least square prenucleolus and the least square nucleolus. Int. J. Game Theory 25, 113–134 (1996)

    Article  MATH  Google Scholar 

  3. Ruiz, L.M., Valenciano, F., Zarzuelo, J.M.: The family of least square values for transferable utility games. Games Econ. Behav. 24, 109–130 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ruiz, L.M., Valenciano, F., Zarzuelo, J.M.: Some new results on least square values for TU games. TOP 6, 139–158 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Moulin, H.: The separability axiom and equal-sharing methods. J. Econ. Theory 36, 120–148 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  6. Shapley, L.S.: A value for \(n\)-person games. Ann. Math. Stud. 28, 307–317 (1953)

    MathSciNet  MATH  Google Scholar 

  7. Branzei, R., Dimitrov, D., Tijs, S.: Models in cooperative game theory. OR Spectr. 7, 19–26 (2008)

    MATH  Google Scholar 

  8. Malawski, M.: “Procedural” values for cooperative games. Int. J. Game Theory 42, 305–324 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nowak, A., Radzik, T.: A solidarity value for \(n\)-person TU games. Int. J. Game Theory 23, 43–48 (1994)

    Article  MATH  Google Scholar 

  10. Driessen, T.S.H., Funaki, Y.: Coincidence of and collinearity between game theoretic solutions. OR Spectr. 13, 15–30 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  11. Xu, G., van den Brink, R., van der Laan, G., Sun, H.: Associated consistency characterization of two linear values for TU games by matrix approach. Linear Algebra Appl. 471, 224–240 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hwang, Y.-A.: Associated consistency and equal allocation of nonseparable costs. Econ. Theory 28, 709–719 (2006). doi:10.1007/s00199-005-0640-7

    Article  MathSciNet  MATH  Google Scholar 

  13. Hamiache, G.: Associated consistency and Shapley value. Int. J. Game Theory 30, 279–289 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ju, Y., Wettstein, D.: Implementing cooperative solution concepts: a generalized bidding approach. Econ. Theory 39, 307–330 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. van den Brink, R.: Null or nullifying players: the difference between the Shapley value and the equal division solutions. J. Econ. Theory 136, 767–775 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Casajus, A., Huettner, F.: Null, nullifying, or dummifying players: the difference between the Shapley value, the equal division value, and the equal surplus division value. Econ. Lett. 122, 167–169 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Driessen, T.S.H.: Cooperative Games, Solutions and Applications. Kluwer, Dordrecht (1988)

    Book  MATH  Google Scholar 

  18. Tijs, S.H.: Bouns for the core and the \(\tau \)-value. In: Moeschlin, O., Pallaschke, D. (eds.) Game Theory and Mathematical Economics, pp. 123–132. North-Holland, Amasterdam (1981)

    Google Scholar 

  19. Gillies, D.B.: Some theorems on \(n\)-person games. Ph.D. Thesis, Princeton University Press, Princeton (1953)

  20. Harsanyi, J.C.: A bargaining model for cooperative \(n\)-person games. In: Tucker, A.W., Luce, R.D. (eds.) Contributions to the Theory of Games IV, pp. 325–355. Priceton University Press, Priceton (1959)

    Google Scholar 

  21. Young, H.P.: Monotonic solutions of cooperative games. Int. J. Game Theory 14, 65–72 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  22. Banzhaf, J.F.: Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev. 19, 317–343 (1965)

    Google Scholar 

Download references

Acknowledgements

We are very grateful to the associate editor and two anonymous referees. Their valuable comments and suggestions contributed to a substantial improvement of the paper. We are also very grateful to Dr. Harry Aarts from University of Twente and Dr. Artem Sedakov from St. Petersburg State University who help us improve the use of the language. This work is supported by National Science Foundation of China (NSFC) through Grant Nos. 71601156, 71671140 and 71571143 as well as Shaanxi Province Science and Technology Research and Development Program (No. 2016JQ7008).

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, No. 127, Youyixilu, Xi’an, China

    Panfei Sun, Dongshuang Hou & Hao Sun

  2. Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Theo Driessen

Authors
  1. Panfei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongshuang Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hao Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Theo Driessen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dongshuang Hou.

Additional information

Communicated by Kyriakos G. Vamvoudakis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, P., Hou, D., Sun, H. et al. Optimization Implementation and Characterization of the Equal Allocation of Nonseparable Costs Value. J Optim Theory Appl 173, 336–352 (2017). https://doi.org/10.1007/s10957-017-1092-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-017-1092-5

Keywords

Mathematics Subject Classification

Search

Navigation