A Dynamic Solution Concept to Cooperative Games with Fuzzy Coalitions

Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 50)

Abstract

The problem of distribution of payoffs through negotiation among the players in a cooperative game with fuzzy coalitions is considered. It is argued that this distribution is influenced by satisfaction of the players in regard to better performance and success within a cooperative endeavour. As a possible alternative to static solutions where this point is ignored, a framework concerning the players’ satisfactions upon receiving an allocation of the worth is studied. A solution of the negotiation process is defined and the corresponding convergence theorem is established.

Keywords

Assure Expense Nash Alloca 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aubin, J.P.: MathematicalMethods of Game and Economic Theory (rev. ed.)., North-Holland, Amsterdam (1982).Google Scholar
  2. 2.
    Azrieli, Y., Lehrer, E.: On some families of cooperative fuzzy games, Int. J. Game Theory, 36, 1–15 (2007)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Borkotokey, S.: Cooperative games with fuzzy coalitions and fuzzy characteristic functions, Fuzzy Sets Syst., 159, 138–151 (2008)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Branzei, R., Dimitrov, D., Tijs, S.: Models in Cooperative Game Theory: Crisp, Fuzzy and Multichoice Games, Lecture Notes in Economics and Mathematical Systems, Springer, 556, Berlin (2004)Google Scholar
  5. 5.
    Butnariu, D.: Stability and Shapley value for an n-persons fuzzy game, Fuzzy Sets Syst. 4, 63–72 (1980)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Carmichael, F.: A Guide to Game Theory, Pearson Education Limited, Prentice Hall, Upper Saddle River (2005)Google Scholar
  7. 7.
    Dieckmann, T.: Dynamic coalition formation and the core, J. Econ. Behav. Org., 49, 3, 363–380 (2002)CrossRefGoogle Scholar
  8. 8.
    Friedman, J.W.: Game Theory with Applications to Economics, Oxford University Press, New York (1986)Google Scholar
  9. 9.
    Furnham, A., Forde, L., Kirsti, K.: Personality and work motivation, Personality Individual Differences, 26, 1035–1043 (1999)CrossRefGoogle Scholar
  10. 10.
    Lai, K.R., Lin, M.W.: Modeling agent negotiation via fuzzy constraints in e-business, Comput. Intell., 20, 4, (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lehrer, E.: Allocation processes in cooperative games, Int. J. Game Theory, 31, 651–654 (2002)Google Scholar
  12. 12.
    Li, S., Zhang, Q.: A simplified expression of the Shapley function for fuzzy game, European J. Oper. Res., 196, 234–245 (2009)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Lim C.S., Zain Mohamed M.: Criteria of project success: An exploratory re-examination, Int. J. Project Manage., 17, 243–248 (1999)CrossRefGoogle Scholar
  14. 14.
    Luo, X., Jennings, N.R., Shadbolt, H., Leung, F., Lee, J.H.M.: A fuzzy constraint based model for bilateral multi-issue negotiations in semi competitive environments, Artif. Intell., 148, 53–102 (2003)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Mares, M., Vlach, M.: Fuzzy coalitional structures, Math. Soft Comput. XIII, 1, 59–70 (2006)MathSciNetGoogle Scholar
  16. 16.
    Mich, L., Fedrizzi, M., Garigliano, R.: Negotiation and Conflict Resolution in Production Engineering Through Source Control, Fuzzy Logic and Soft Computing (Ed.), Advances in Fuzzy Systems-Applications and Theory 4, World Scientific, Singapore, 181–188 (1995)Google Scholar
  17. 17.
    Nash, J.F.: The bargaining problem, Econometrica, 18, 155–162 (1950)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Ray, D., Vohra, R.: Equilibrium binding agreements. J. Econ. Theory, 73, 30–78 (1997)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Ray, D., Vohra, R.: A theory of endogenous coalition structure, Games Econ. Behav., 26, 286–336 (1999)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Ray, D., Vohra, R.: Coalitional power and public goods. J. Pol. Econ. 109, 1355–1384 (2001)CrossRefGoogle Scholar
  21. 21.
    Tohme, F., Sandholm, T.: Coalition formation process with belief revision among bounded self interested agents, (Source: Internet, Open access article).Google Scholar
  22. 22.
    Tsurumi, M., Tanino, T., Inuiguchi, M.: Theory and methodology–A Shapley function on a class of cooperative fuzzy games, European J. Oper. Res., 129, 596–618 (2001)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Yager, R.: Multiagent negotiation using linguistically expressed mediation rules, Group Decision Negotiation, 16 1–23 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsDibrugarh UniversityAssamIndia

Personalised recommendations