Advertisement

Soft Computing

, Volume 22, Issue 17, pp 5719–5724 | Cite as

Stable set of uncertain coalitional game with application to electricity suppliers problem

  • Yajuan Liu
  • Gang Liu
Focus

Abstract

Coalitional game deals with the situation that involves cooperations among the players. When the payoffs are characterized by uncertain variables, classical coalitional game evolves to uncertain coalitional game. Some solutions of uncertain coalitional game have been proposed such as core and Shapley value. This paper goes further to present another concept of solution—stable set for uncertain coalitional game, and shows that the core is the subset of the stable set in an uncertain coalitional game. Finally, an electricity suppliers cooperation problem is analyzed by the stable set in uncertain coalitional game.

Keywords

Uncertain variable Coalitional game Stable set Electricity suppliers problem 

Notes

Acknowledgements

Funding was provided by National Natural Science Foundation of China (Grant No. 61374082 ).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Aubin JP (1981) Cooperative fuzzy games. Math Oper Res 6(1):1–13MathSciNetCrossRefMATHGoogle Scholar
  2. Aumann R, Maschler M (1964) The bargaining set for cooperative games. Adv Game Theory 52:443–476MathSciNetMATHGoogle Scholar
  3. Blau RA (1974) Random-payoff two-person zero-sum games. Oper Res 22(6):1243–1251MathSciNetCrossRefMATHGoogle Scholar
  4. Cassidy RG, Field CA, Kirby M (1972) Solution of a satisficing model for random payoff games. Manag Sci 19:266–271MathSciNetCrossRefMATHGoogle Scholar
  5. Charnes AC, Kirby M, Raike W (1968) Zero–zero chance-constrained games. Theory Probab Appl 13(4):628–646MathSciNetCrossRefMATHGoogle Scholar
  6. Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604CrossRefMATHGoogle Scholar
  7. Gao J (2007) Credibilistic game with fuzzy information. J Uncertain Syst 1(1):74–80Google Scholar
  8. Gao J (2013) Uncertain bimatrix game with application. Fuzzy Optim Decis Mak 12(1):65–78MathSciNetCrossRefGoogle Scholar
  9. Gao R (2016) Milne method for solving uncertain differential equations. Appl Math Comput 274:774–785MathSciNetGoogle Scholar
  10. Gao J, Yang X (2013) Credibilistic bimatrix game with asymmetric information and Bayesian optimistic equilibrium strategy. Int J Uncertain Fuzz 21(supp01):89–100MathSciNetCrossRefMATHGoogle Scholar
  11. Gao J, Yu Y (2013) Credibilistic extensive game with fuzzy payoffs. Soft Comput 17(4):557–567CrossRefMATHGoogle Scholar
  12. Gao J, Liu ZQ, Shen P (2009) On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game. Soft Comput 13(2):127–132CrossRefMATHGoogle Scholar
  13. Gao J, Zhang Q, Shen P (2011) Coalitional game with fuzzy payoffs and credibilistic Shapley value. Iran J Fuzzy Syst 8(4):107–117MathSciNetMATHGoogle Scholar
  14. Gao J, Yang X, Liu D (2016) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput. doi: 10.1016/j.asoc.2016.06.018 Google Scholar
  15. Harsanyi JC (1995) Games with incomplete information. Am Econ Rev 85:291–303Google Scholar
  16. Liang R, Yu Y, Gao J, Liu ZQ (2010) \(N\)-person credibilistic strategic game. Front Comput Sci China 4(2):212–219CrossRefMATHGoogle Scholar
  17. Liu B (2007) Uncertainty theory, 2nd edn. Springer, BerlinMATHGoogle Scholar
  18. Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinCrossRefGoogle Scholar
  19. Liu B (2013) Toward uncertain finance theory. J Uncertain Anal Appl 1Google Scholar
  20. Liu B (2015) Uncertainty theory, 5th edn. Springer, BerlinMATHGoogle Scholar
  21. Liu Y, Chen X, Ralescu DA (2015) Uncertain currency model and currency option pricing. Int J Intell Syst 30(1):40–51CrossRefGoogle Scholar
  22. Osborne MJ, Rubinstein A (1994) A course in game theory. The MIT Press, LondonMATHGoogle Scholar
  23. Schmeidler D (1969) The nucleolus of a characteristic function game. SIMA J Appl Math 17(6):1163–1170MathSciNetCrossRefMATHGoogle Scholar
  24. Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in committee system. Am Polit Sci Rev 48:787–792CrossRefGoogle Scholar
  25. Shen P, Gao J (2011) Coalitional game with fuzzy information and credibilistic core. Soft Comput 15(4):781–786CrossRefMATHGoogle Scholar
  26. von Neumann J, Morgenstern O (1944) The theory of games and economic behavior. Princeton University Press, PrincetonMATHGoogle Scholar
  27. Wang X, Ning Y, Moughal TA, Chen X (2015) Adams–Simpson method for solving uncertain differential equation. Appl Math Comput 271:209–219MathSciNetGoogle Scholar
  28. Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertainty Anal Appl 1(Article 17)Google Scholar
  29. Yang X, Gao J (2014) Uncertain core for coalitional game with uncertain payoffs. J Uncertain Syst 8(1):13–21Google Scholar
  30. Yang X, Gao J (2016) Linear-quadratic uncertain differential game with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826CrossRefGoogle Scholar
  31. Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525CrossRefGoogle Scholar
  32. Yang X, Ralescu DA (2015) Adams method for solving uncertain differential equations. Appl Math Comput 270:993–1003MathSciNetGoogle Scholar
  33. Yang X, Shen Y (2015) Runge-Kutta method for solving uncertain differential equations. J Uncertainty Anal Appl 3Google Scholar
  34. Yang X, Yao K (2016) Uncertain partial differential equation with application to heat conduction. Fuzzy Optim Decis Mak. doi: 10.1007/s10700-016-9253-9 Google Scholar
  35. Yao K (2016) Uncertain differential equations. Springer, BerlinCrossRefMATHGoogle Scholar
  36. Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst 41(7):535–547CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Donlinks School of Economics and ManagementUniversity of Science and Technology BeijingBeijingChina
  2. 2.School of Economics and ManagementBeijing Information Science and Technology UniversityBeijingChina
  3. 3.School of InformationRenmin University of ChinaBeijingChina

Personalised recommendations