Compromise in cooperative game and the VIKOR method
DOI:
https://doi.org/10.2298/YJOR0902225OKeywords:
multicriteria decision making, cooperative game, compromise, VIKOR methodAbstract
Five approaches in conflict resolution are distinguished, based on cooperativeness and aggressiveness in resolving conflict. Compromise based on cooperativeness is emphasized here as a solution in conflict resolution. Cooperative game theory oriented towards aiding the conflict resolution is considered and the compromise value for TU(transferable utility)-game is presented. The method VIKOR could be applied to determine compromise solution of a multicriteria decision making problem with noncommensurable and conflicting criteria. Compromise is considered as an intermediate state between conflicting objectives or criteria reached by mutual concession. The applicability of the cooperative game theory and the VIKOR method for conflict resolution is illustrated.References
Bell, D.E., Raiffa, H., and Tversky, A., “Descriptive, normative, and prescriptive interactions in decision making,” in: E. David, D.E. Bell, H. Raiffa, and A. Tversky (eds.), Decision Making: Descriptive, Normative, and Prescriptive Interactions, Cambridge University Press, Cambridge, 1985, 9-30.
Bilbao, J.M., Jiménez-Losada, A., Lebrón, E., and Tijs, S.H., “The τ-value for games on matroids,” TOP, Springer, Berlin / Heidelberg, 10 (1) (2002), 67-81.
Branzei, R., Dimitrov, D., and Tijs, S., “Hypercubes and compromise values for cooperative fuzzy games,” European Journal of Operational Research, 155 (3) (2004) 733–740.
Butler, L.C.T., and Rothstein, A., “On conflict and consensus,” [Online]. Available: http://www.consensus.net.
Curiel, I., Cooperative Game Theory and Applications, Kluwer Academic Publishers, Boston, 1997.
Duckstein, L., and Opricovic, S., “Multiobjective optimization in river basin development,” Water Resources Research, 16 (1) (1980) 14-20.
Escobar, M.T., and Moreno-Jimenez, J.M., “A linkage between the Analytic Hierarchy Process and the Compromise Programming Models,” Omega, 30 (5) (2002) 359–365.
Fang, L., Hipel, K.W., and Kilgour, D.M., Interactive Decision Making: The Graph Model for Conflict Resolution, Wiley, New York, 1993.
Ferguson, T., “Game theory: Games in coalitional form,” [Online]. Available: http://www.math.ucla.edu/~tom/Game_Theory/coal.pdf.
Fraser, N.M., and Hipel, K.W., Conflict Analysis: Models and Resolutions, North Holland, New York, 1984.
Hanany, E., Kilgour, D. M., Gerchak, Y., “Final-offer arbitration and risk aversion in bargaining,” Management Science, INFORMS Publications, 53 (11) (2007) 1785-1792.
Jelassi, M.T., Kersten, G.E., and Zionts, S., “An introduction to group decision and negotiation support,” in: C. Bana e Costa (ed.), Readings in Multiple Criteria Decision Aid, Springer Verlag, Heidelberg, 1990, 537–568.
Kersten, G.E., “Support for group decisions and negotiations - An overview,” in: J. Climaco (ed.), Multicriteria Analysis, Springer- Verlag, 1997, 332-346.
Murphy, P., “Game theory models for organizational/public conflict,” Canadian Journal of Communication, 16 (2) (1991), [Online]. Available: http://www.cjc-online.ca/archive.php.
Opricovic, S., and Tzeng, G.H., “The compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS,” European Journal of Operational Research, 156 (2) (2004) 445-455.
Opricovic, S., and Tzeng, G.H., “Extended VIKOR method in comparison with outranking methods,” European Journal of Operational Research, 178 (2) (2007) 514–529.
Pareto, V., Cours d’Economie Politique, Droz, Geneva, 1896.
Quant, M., Borm, P., Reijnierse, H., and van Velzen, B., “Compromise stable TU-games,” Discussion paper No.2003-55, Tilburg University, 2003.
Tijs, S., and Otten, G., “Compromise values in cooperative game theory,” Top, 1 (1) (1993) 1-51.
Timmer, J., “The compromise value for cooperative games with random payoffs,” Mathematical Methods of Operations Research, Physica Verlag, 64 (1) (2005) 95-106.
Yu, P.L., “A class of solutions for group decision problems,” Management Science, 19 (8) (1973) 936-946.
Yu, P.L., Forming Winning Strategies: An Integrated Theory of Habitual Domains, Springer Verlag, Heidelberg, 1990.
Zadeh, L.A., “Optimality and non-scalar-valued performance criteria,” IEEE Transactions on Automatic Control, AC-8 (1) (1963) 59-60.
Downloads
Published
Issue
Section
License
Copyright (c) 2009 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
