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

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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.

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References

  • Aubin JP (1981) Cooperative fuzzy games. Math Oper Res 6(1):1–13

    Article  MathSciNet  MATH  Google Scholar 

  • Aumann R, Maschler M (1964) The bargaining set for cooperative games. Adv Game Theory 52:443–476

    MathSciNet  MATH  Google Scholar 

  • Blau RA (1974) Random-payoff two-person zero-sum games. Oper Res 22(6):1243–1251

    Article  MathSciNet  MATH  Google Scholar 

  • Cassidy RG, Field CA, Kirby M (1972) Solution of a satisficing model for random payoff games. Manag Sci 19:266–271

    Article  MathSciNet  MATH  Google Scholar 

  • Charnes AC, Kirby M, Raike W (1968) Zero–zero chance-constrained games. Theory Probab Appl 13(4):628–646

    Article  MathSciNet  MATH  Google Scholar 

  • Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604

    Article  MATH  Google Scholar 

  • Gao J (2007) Credibilistic game with fuzzy information. J Uncertain Syst 1(1):74–80

    Google Scholar 

  • Gao J (2013) Uncertain bimatrix game with application. Fuzzy Optim Decis Mak 12(1):65–78

    Article  MathSciNet  Google Scholar 

  • Gao R (2016) Milne method for solving uncertain differential equations. Appl Math Comput 274:774–785

    MathSciNet  Google Scholar 

  • Gao J, Yang X (2013) Credibilistic bimatrix game with asymmetric information and Bayesian optimistic equilibrium strategy. Int J Uncertain Fuzz 21(supp01):89–100

    Article  MathSciNet  MATH  Google Scholar 

  • Gao J, Yu Y (2013) Credibilistic extensive game with fuzzy payoffs. Soft Comput 17(4):557–567

    Article  MATH  Google Scholar 

  • Gao J, Liu ZQ, Shen P (2009) On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game. Soft Comput 13(2):127–132

    Article  MATH  Google Scholar 

  • Gao J, Zhang Q, Shen P (2011) Coalitional game with fuzzy payoffs and credibilistic Shapley value. Iran J Fuzzy Syst 8(4):107–117

    MathSciNet  MATH  Google Scholar 

  • 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 

  • Harsanyi JC (1995) Games with incomplete information. Am Econ Rev 85:291–303

  • Liang R, Yu Y, Gao J, Liu ZQ (2010) \(N\)-person credibilistic strategic game. Front Comput Sci China 4(2):212–219

    Article  MATH  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin

    Book  Google Scholar 

  • Liu B (2013) Toward uncertain finance theory. J Uncertain Anal Appl 1

  • Liu B (2015) Uncertainty theory, 5th edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu Y, Chen X, Ralescu DA (2015) Uncertain currency model and currency option pricing. Int J Intell Syst 30(1):40–51

    Article  Google Scholar 

  • Osborne MJ, Rubinstein A (1994) A course in game theory. The MIT Press, London

    MATH  Google Scholar 

  • Schmeidler D (1969) The nucleolus of a characteristic function game. SIMA J Appl Math 17(6):1163–1170

    Article  MathSciNet  MATH  Google Scholar 

  • Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in committee system. Am Polit Sci Rev 48:787–792

    Article  Google Scholar 

  • Shen P, Gao J (2011) Coalitional game with fuzzy information and credibilistic core. Soft Comput 15(4):781–786

    Article  MATH  Google Scholar 

  • von Neumann J, Morgenstern O (1944) The theory of games and economic behavior. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Wang X, Ning Y, Moughal TA, Chen X (2015) Adams–Simpson method for solving uncertain differential equation. Appl Math Comput 271:209–219

    MathSciNet  Google Scholar 

  • Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertainty Anal Appl 1(Article 17)

  • Yang X, Gao J (2014) Uncertain core for coalitional game with uncertain payoffs. J Uncertain Syst 8(1):13–21

    Google Scholar 

  • Yang X, Gao J (2016) Linear-quadratic uncertain differential game with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826

    Article  Google Scholar 

  • Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525

    Article  Google Scholar 

  • Yang X, Ralescu DA (2015) Adams method for solving uncertain differential equations. Appl Math Comput 270:993–1003

    MathSciNet  Google Scholar 

  • Yang X, Shen Y (2015) Runge-Kutta method for solving uncertain differential equations. J Uncertainty Anal Appl 3

  • 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 

  • Yao K (2016) Uncertain differential equations. Springer, Berlin

    Book  MATH  Google Scholar 

  • Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst 41(7):535–547

    Article  MATH  Google Scholar 

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Acknowledgements

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

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Correspondence to Gang Liu.

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Communicated by Y. Ni.

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Liu, Y., Liu, G. Stable set of uncertain coalitional game with application to electricity suppliers problem. Soft Comput 22, 5719–5724 (2018). https://doi.org/10.1007/s00500-017-2611-x

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