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Group Decision and Negotiation

, Volume 21, Issue 4, pp 439–459 | Cite as

Allocating Profit Among Rational Players in a Fuzzy Coalition: A Game Theoretic Model

  • Surajit BorkotokeyEmail author
  • Rupok Neog
Article

Abstract

In this paper, the problem of allocation of the profit, obtained from a fuzzy coalition, among its players is considered. It is argued that this allocation is influenced by satisfaction of the players in regards to better performance and success within a cooperative endeavour. Our model is based on the real life situations, where possibly one or more players compromise on their payoffs in order to help forming a coalition. We have developed a dynamic approach to obtain a suitable solution to the corresponding cooperative fuzzy game. Further, the notion of a penalty among the bargaining players is introduced. This would inflict them to reasonable demands only.

Keywords

Fuzzy coalitions Rational player Exact offer Penalty 

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References

  1. Aubin JP (1982) Mathematical methods of game and economic theory (rev. ed.). North-Holland, AmsterdamGoogle Scholar
  2. Azrieli Y, Lehrer E (2007) On some families of cooperative fuzzy games. Int J Game Theory 36: 1–15CrossRefGoogle Scholar
  3. Borkotokey S (2008) Cooperative games with fuzzy coalitions and fuzzy characteristic functions. Fuzzy Sets Syst 159: 138–151CrossRefGoogle Scholar
  4. Borkotokey S (2008) Modelling a solution concept to cooperative games with fuzzy coalitions through negotiation via mediator. Math Forum Spl. vol. XXI: 33–40Google Scholar
  5. Borkotokey S (accepted) A dynamic solution concept to cooperative games with fuzzy coalitions, book article. In: Mishra SK (ed) Indian contribution to non-convex optimization. Springer, BerlinGoogle Scholar
  6. Branzei R, Dimitrov D, Tijs S (2004) Models in cooperative game theory: crisp, fuzzy and multichoice games, lecture notes in economics and mathematical systems. Springer, Berlin, p 556Google Scholar
  7. Butnariu D (1980) Stability and shapley value for an n-persons fuzzy game. Fuzzy Sets Syst 4: 63–72CrossRefGoogle Scholar
  8. Carmichael F (2005) A guide to game theory. Pearson Education Limited, Prentice HallGoogle Scholar
  9. Dieckmann T (2002) Dynamic coalition formation and the core. J Econ Behav Organ 49(3): 363–380CrossRefGoogle Scholar
  10. Dubois D, Prade H (1988) Fuzzy numbers :an overview. In: Bezdek JC (eds) Analysis of fuzzy information. CRC, Boca Raton, pp 3–39Google Scholar
  11. Friedman JW (1986) Game theory with applications to economics. Oxford University Press, New YorkGoogle Scholar
  12. Furnham A, Forde L, Kirsti F (1999) Personality and work motivation. Pers Individ Dif 26: 1035–1043CrossRefGoogle Scholar
  13. Lai KR, Lin MW (2004) Modeling agent negotiation via fuzzy constraints in e-business. Comput Intell 20(4)Google Scholar
  14. Lehrer E (2002) Allocation processes in cooperative games. Int J Game Theory 31: 651–654Google Scholar
  15. Li S, Zhang Q (2009) A simplified expression of the shapley function for fuzzy game. Eur J Oper Res 196: 234–245CrossRefGoogle Scholar
  16. Lim CS, Zain Mohamed M (1999) Criteria of project success: an exploratory re-examination. Int J Project Manag 17(4): 243–248CrossRefGoogle Scholar
  17. Luo X, Jennings NR, Shadbolt H, Leung F, Lee JHM (2003) A fuzzy constraint based model for bilateral multi-issue negotiations in semi competitive environments. Artif Intell 148: 53–102CrossRefGoogle Scholar
  18. Mares M, Vlach M (2001) Linear coalition games and their fuzzy extensions. Int J Uncertain Fuzziness Knowl Based Syst 9: 341–354Google Scholar
  19. Mares M, Vlach M (2006) Fuzzy coalitional structures. Mathware Soft Comput XIII(1): 59–70Google Scholar
  20. Mich L, fedrizzi M, Garigliano R (1995) Negotiation and conflict resolution in production engineering through source control. Fuzzy Logic Soft Comput (ed) Advances in fuzzy systems—applications and theory, vol 4. World Scientific, Singapore, pp 181–188Google Scholar
  21. Nash JF (1950) The bargaining problem. Econometrica 18:155–162 [312]Google Scholar
  22. Ray D, Vohra R (1997) Equilibrium binding agreements. J Econ Theory 73: 30–78CrossRefGoogle Scholar
  23. Ray D, Vohra R (1999) A theory of endogenous coalition structure. Games Econ Behav 26: 286–336CrossRefGoogle Scholar
  24. Ray D, Vohra R (2001) Coalitional power and public goods. J Pol Econ 109: 1355–1384CrossRefGoogle Scholar
  25. Romero Cortes JC, Sheremotov LB (2002) Model of cooperation in multi-agent systems with fuzzy coalitions CEEMAS 2001. LNAI 2296: 263–272Google Scholar
  26. Tohme F, Sandholm T (in press) Coalition formation process with belief revision among bounded self interested agents. (Source : Internet, Open access Journal)Google Scholar
  27. Tsurumi M, Tanino T, Inuiguchi M (2001) Theory and methodology—a shapley function on a class of cooperative fuzzy games. Eur J Oper Res 129: 596–618CrossRefGoogle Scholar
  28. Yager R (2007) Multiagent negotiation using linguistically expressed mediation rules. Group Decis Negot 16: 1–23CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsDibrugarh UniversityDibrugarhIndia

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