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Core, least core and nucleolus for multiple scenario cooperative games. (English) Zbl 1132.91332

Summary: Multiple scenario cooperative games model situations where the worth of the coalitions is valued in different scenarios simultaneously or under different states of nature. In this paper we analyze solution concepts for this class of games keeping the multidimensional nature of the characteristic function. We obtain extensions of the notions of core, least core and nucleolus, and explore the relationship among these solution concepts.

MSC:

91A12 Cooperative games

Software:

ADBASE
Full Text: DOI

References:

[1] Aumann, R. J.; Maschler, M., Game theoretic analysis of a bankruptcy problem from the Talmud, Journal of Economic Theory, 36, 195-213 (1985) · Zbl 0578.90100
[2] Derks, J. M.; Tijs, S. H., Stable outcome for multi-commodity flow games, Methods of Operations Research, 55, 493-504 (1986) · Zbl 0572.90024
[3] Fernández, F. R.; Hinojosa, M. A.; Mármol, A. M.; Puerto, J., Solution concepts in multiple criteria linear production games, (Trzaskalik, T.; Michnik, J., Multiple Objective and Goal Programming. Recent Developments. Advances in Soft Computing (2002), Physica-Verlag), 257-271 · Zbl 1038.90039
[4] Fernández, F. R.; Hinojosa, M.; Puerto, J., Core solutions in vector-valued games, Journal of Optimization Theory and Applications, 112, 331-360 (2002) · Zbl 1005.91016
[5] Fernández, F.R., Hinojosa, M., Puerto, J., in press. Set valued TU-games. European Journal of Operational Research; Fernández, F.R., Hinojosa, M., Puerto, J., in press. Set valued TU-games. European Journal of Operational Research · Zbl 1067.90068
[6] Gow, S. H.; Thomas, L. C., Interchange fees for bank ATM networks, Naval Research Logistic, 45, 407-417 (1998) · Zbl 0936.91005
[7] Jörnsten, K., Lind, M., Tind, J., 1995. Stable payment schemes of TU-games with multiple criteria. Revised version of Publication 93, 3, Department of Operations Research, University of Aarhus, Arhus, Denmark; Jörnsten, K., Lind, M., Tind, J., 1995. Stable payment schemes of TU-games with multiple criteria. Revised version of Publication 93, 3, Department of Operations Research, University of Aarhus, Arhus, Denmark
[8] Littlechild, S. C.; Thompson, G. F., Aircraft landing fees: A game theory approach, The Bell Journal of Economics, 8, 186-204 (1977)
[9] Mármol, A. M.; Puerto, J.; Fernández, F. R., The use of partial information on weights in multicriteria decision problems, Journal of Multi-criteria Decision Analysis, 7, 322-329 (1998) · Zbl 0917.90212
[10] Mármol, A. M.; Puerto, J.; Fernández, F. R., Sequential incorporation of imprecise information in multiple criteria decision processes, European Journal of Operational Research, 137, 123-133 (2002) · Zbl 1009.90058
[11] Maschler, M., The bargaining set, kernel and nucleolus, (Aumann, R. J.; Hart, S., Handbook of Game Theory with Economics Applications, vol. I (1992), Elsevier Science Publishers: Elsevier Science Publishers Amsterdam) · Zbl 0968.91502
[12] Nishizaki, I.; Sakawa, M., Fuzzy and Multiobjective Games for Conflict Resolution (2001), Physica-Verlag · Zbl 0973.91001
[13] Nouweland, A.; van den Aarts, H.; Borm, P., Multi-commodity games, Methods of Operations Research, 63, 329-338 (1989) · Zbl 0726.90102
[14] Schmeidler, D., The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics, 16, 1163-1170 (1969) · Zbl 0191.49502
[15] Steuer, R.E., 1995. Manual for the ADBASE. Multiple objective linear programming package. University of Georgia, Athens, GA; Steuer, R.E., 1995. Manual for the ADBASE. Multiple objective linear programming package. University of Georgia, Athens, GA
[16] Voorneveld, M., Van den Nouweland, A., 1998. Cooperative multicriteria games with public and private criteria: An investigation of core concepts. CentER Discussion Paper Series 1998, 62, Tilburg University; Voorneveld, M., Van den Nouweland, A., 1998. Cooperative multicriteria games with public and private criteria: An investigation of core concepts. CentER Discussion Paper Series 1998, 62, Tilburg University
[17] Young, H. P., Cost allocation, (Young, H. P., Fair Allocation Proceedings of Symposia in Applied Mathematics, vol. 33 (1985), American Mathematical Society: American Mathematical Society Providence, RI), 69-94 · Zbl 0925.90085
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