Dynamic resource allocation in fuzzy coalitions : a game theoretic model

Neog, Rupok and Borkotokey, Surajit (2011): Dynamic resource allocation in fuzzy coalitions : a game theoretic model.

Abstract

We introduce an efficient and dynamic resource allocation mechanism within the framework of a cooperative game with fuzzy coalitions. A fuzzy coalition in a resource allocation problem can be so defined that membership grades of the players in it, are proportional to the fractions of their total resources. We call any distribution of the resources possessed by the players, among a prescribed number of coalitions, a fuzzy coalition structure and every membership grade (equivalently fraction of the total resource), a resource investment. It is shown that this resource investment is influenced by satisfaction of the players in regards to better performance under a cooperative setup. Our model is based on the real life situations, where possibly one or more players compromise on their resource investments in order to help forming a coalition.

• Item Type: MPRA Paper
• Language: English
• Keywords: fuzzy coalitions; rational player; exact resource allocation; cooperative game
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

[1] J. P. Aubin, 1982. Mathematical Methods of Game and Economic Theory' (rev. ed.)., North-Holland, Ams- terdam.

[2] Y. Azrieli, E. Lehrer, 2007, On some families of cooperative fuzzy games, International Journal of Game Theory,36, 1-15.

[3] S. Borkotokey, 2008. Cooperative Games with fuzzy coalitions and fuzzy characteristic functions, Fuzzy Sets and Systems, Elsevier, 159, 138{151.

[4] S. Borkotokey, 2008-09. Modelling a Solution concept to cooperative games with fuzzy coalitions through negotiation via mediator, Mathematical Forum, Spl.Vol. XXI, 33-40.

[5] S. Borkotokey, 2011. A Dynamic Solution concept to cooperative games with fuzzy coalitions, Chapter 13(Book Article), Topics in non-convex optimization: Theory and Applications; Springer Optimization and its Applications 50, Ed. S.K. Mishra, 215-229, Springer.

[6] S. Borkotokey, R.Neog, 2010. Allocating Prot Among Rational Players in a Fuzzy Coalition:A Game Theoretic Model,Group Decision and Negotiation, (available online) DOI 10.1007/s 10726-010-9217-3, Springer-Verlag.

[7] R. Branzei, D. Dimitrov, S. Tijs, 2004. Models in Cooperative Game Theory: Crisp, Fuzzy and Multichoice Games, Lecture Notes in Economics and Mathematical Systems, Springer , 556, Berlin.

[8] D. Butnariu, 1980. Stability and Shapley value for an n-persons fuzzy game, Fuzzy Sets and Systems 4, 63-72.

[9] F. Carmichael, 2005. A Guide to Game Theory,Pearson Education Limited, Prentice Hall.

[10] J.C.Romero Cortes, L.B. Sheremotov, 2002. Model of Cooperation in Multi-agent systems with fuzzy coali- tions, CEEMAS 2001,LNAI 2296,263-272.

[11] T. Dieckmann, 2002. Dynamic coalition formation and the core, Journal of Economic Behaviour and Organization, Vol.49, 3,363-380.

[12] D. Dubois, H. Prade, 1988. Fuzzy Numbers :An Overview, Analysis of Fuzzy Information (J.C. Bezdek, ed.),CRC Press,Boca Raton,3-39.

[13] J. W. Friedman ,1986. Game Theory with Applications to Economics, NY: Oxford University Press.

[14] A. Furnham, L. Forde, F. Kirsti, 1999. Personality and work motivation, Personality and Individual Dierences,26,1035-1043.

[15] K .R Lai, M .W.Lin, 2004. Modeling Agent Negotiation via Fuzzy Constraints in E-Business, Computational Intelligence, Vol. 20, Number 4.

[16] E. Lehrer, 2002. Allocation processes in cooperative games, Int J Game Theory, 31, 651-654.

[17] S. Li, Q. Zhang, 2009. A simplied expression of the Shapley function for fuzzy game, European Journal of Operational Research, 196 ,234-245.

[18] C. S. Lim, M. Zain Mohamed, 1999. Criteria of project success: an exploratory re-examination,International Journal of Project Management,Volume 17, Issue 4, 243-248.

[19] X. Luo, N.R. Jennings, H. Shadbolt,F. Leung,J.H.M. Lee, 2003. Afuzzy constraint based model for bilateral multi-issue negotiations in semi competitive environments,Articial Intelligence,148,53-102.

[20] M. Mares, M. Vlach, 2006. Fuzzy coalitional structures, Mathware and Soft Comput XIII,1, 59-70.

[21] M. Mares, M. Vlach, 2001. Linear coalition games and their fuzzy extensions. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9, 341-354.

[22] M. Mares, M. Vlach , 2006. Fuzzy Coalitional Structures, Mathware and Soft Computing XIII ,1, 59-70.

[23] L. Mich, M. fedrizzi, R. Garigliano, 1995. Negotiation and Conflict Resolution in Production Engineering Through Source Control, Fuzzy Logic and Soft Computing(Ed.), Advances in Fuzzy Systems- Applications and Theory Vol.4,World Scientic, 181-188.

[24] J. F. Nash, 1950. The Bargaining Problem, Econometrica 18, 155-162.

[25] D. Ray , R. Vohra ,1997. Equilibrium binding agreements. J Econ Theory ,73,30-78.

[26] D. Ray , R. Vohra , 1999. A theory of endogenous coalition structure.Games Econ Behav ,26,286-336.

[27] D. Ray , R. Vohra , 2001. Coalitional power and public goods. J Pol Econ 109, 1355-1384.

[28] F. Tohme, and T. Sandholm, , Coalition Formation Process with belief revision among bounded self interested agents, (Source : Internet, Open access Journal).

[29] M. Tsurumi, T. Tanino, M. Inuiguchi, 2001. Theory and methodology{A Shapley function on a class of cooperative fuzzy games, European Journal of Operation Research, 129 , 596-618.

[30] J. von Neumann, O. Morgenstern, 1944. Theory of Games and Economic Behaviour, New York, Wiley.

[31] R. Yager, 2007. Multiagent negotiation using linguistically expressed mediation rules,Group Decision and Negotiation,16,1-23.