Abstract
In this paper, a cooperative game has been considered, where there is a coalition between rational players in an uncertain environment. The uncertainty occurs in terms of the quality of the raw material. The pay-offs of the players are influenced by the degree of satisfaction. Pay-offs are considered as interval numbers. A multisection technique has been applied to obtain a rational solution. In the process, it has been found that the degree of satisfaction of the rational players converges to its optimum value with the convergence of the iterations. A comparative study has been made with methods existing in the literature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aubin J P 1982 Mathematical methods of game and economic theory (rev. edn.). North-Holland, Amsterdam 7: 1–619
Azrieli Y and Lehrer E 2007 On some families of cooperative fuzzy games. Int. J. Game Theory 36: 1–15
Borkotokey S 2008 Modelling a solution concept to cooperative games with fuzzy coalitions through negotiation via mediator. Math Forum Spl. 21: 33–40
Borkotokey S and Rupok Neog 2012 Allocating profit among rational players in a fuzzy coalition: A game theoretic model. Group Decis. Negot. 21: 439–459
Branzei R, Dimitrov D and Tijs S 2004 Hypercubes and compromise values for cooperative fuzzy games. Eur. J. Oper. Res. 155: 733–740
Branzei R, Dimitrov D and Tijs S 2005 Models in cooperative game theory: crisp, fuzzy and multichoice games. Lecture Notes In Economics and Mathematical Systems. Berlin, Springer, 556
Butnariu D 1980 Stability and shapley value for an n-persons fuzzy game. Fuzzy Sets Syst. 4: 63–72
Dieckmann T 2002 Dynamic coalition formation and the core. J. Econ. Behav. Organ 49: 363–380
Mares M and Vlach M 2001 Linear coalition games and their fuzzy extensions. Int. J. Uncertain Fuzziness Knowledge Based Syst. 9: 341–354
Mares M and Vlach M 2006 Fuzzy coalitional structures. Mathware Soft Computation 13: 59–70
Moore R E 1979 Method and application of interval analysis. SIAM, Philadelphia
Prasun Kumar Nayak, Sibasis Bandyopadhyay and Madhumangal Pal 2014 An algorithm for solution of interval games. Int. J. Oper. Res. 20(2): 207–225
Ray D and Vohra R 1997 Equilibrium binding agreements. J. Econ. Theory 73: 30–78
Ray D and Vohra R 1999 A theory of endogenous coalition structure. Games Econ. Behav. 26: 286–336
Ray D and Vohra R 2001 Coalitional power and public goods. J. Pol. Econ. 109: 1355–1384
Romero Cortes J C and Sheremotov L B 2002 Model of cooperation in multi-agent systems with fuzzy coalitions. CEEMAS, LNAI 2296: 263–272
Sakawa M 1983 Interactive computer programme for fuzzy linear programming with multiple objectives. Int. J. Man-Mach. Stud. 18: 489–503
Seikh M R, Nayak Prasun and Pal M 2013 Notes on triangular intuitionistic fuzzy number. Int. J. Math. Oper. Res. 5(4): 446–465
Shapley L S 1953 A value for n-person games. In: Kuhn H W, Tucker, A W (Eds.), Contributions to the theory of Games II. In: Ann. Math. Stud. 2: 307–317
Xiaodong Liu, Jiuqiang Liu and Cui Li 2013 Average monotonic cooperative fuzzy games. Fuzzy Sets Syst. 231: 95–107
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
BANDYOPADHYAY, S., RAHA, S. & NAYAK, P.K. Profit allocation among rational players in a cooperative game under uncertainty. Sadhana 40, 1077–1089 (2015). https://doi.org/10.1007/s12046-015-0374-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12046-015-0374-6