×

A coalition formation value for games in partition function form. (English) Zbl 1253.91016

Summary: The coalition formation problem in an economy with externalities can be adequately modeled by using games in partition function form (PFF games), proposed by Thrall and Lucas. If we suppose that forming the grand coalition generates the largest total surplus, a central question is how to allocate the worth of the grand coalition to each player, i.e., how to find an adequate solution concept, taking into account the whole process of coalition formation. We propose in this paper the original concepts of scenario-value, process-value and coalition formation value, which represent the average contribution of players in a scenario (a particular sequence of coalitions within a given coalition formation process), in a process (a sequence of partitions of the society), and in the whole (all processes being taken into account), respectively. We give also two axiomatizations of our coalition formation value.

MSC:

91A12 Cooperative games
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Albizuri, M.; Arin, J.; Rubio, J., An axiom system for a value for games in partition function form, International Game Theory Review, 7, 63-72 (2005) · Zbl 1134.91315
[2] Andrews, G. E., The theory of partitions, (Encyclopedia of Mathematics and its Applications, vol. 2 (1976), Addison-Wesley) · Zbl 0155.09302
[3] Bloch, F., Sequential formation of coalitions in games with externalities and fixed payoff divisions, Games and Economic Behavior, 14, 90-123 (1996) · Zbl 0862.90143
[4] Bolger, E. M., A set of axioms for a value for partition function games, International Journal of Game Theory, 18, 37-44 (1989) · Zbl 0671.90107
[5] de Clippel, G.; Serrano, R., Marginal contributions and externalities in the value, Econometrica, 76, 6, 1413-1436 (2008) · Zbl 1152.91340
[6] Diamantoudi, E.; Xue, L., Coalitions, agreements and efficiency, Journal of Economic Theory, 136, 105-125 (2007) · Zbl 1256.91009
[7] Pham Do, K. H.; Norde, H., The Shapley value for partition function form games, International Game Theory Review, 9, 353-360 (2007) · Zbl 1139.91304
[8] Y. Fujinaka, On the marginality principle in partition function form games, Technical report, Kobe University, 2004.; Y. Fujinaka, On the marginality principle in partition function form games, Technical report, Kobe University, 2004.
[9] Funaki, Y.; Yamato, T., The core of an economy with a common pool resource: a partition function approach, International Journal of Game Theory, 28, 157-171 (1999) · Zbl 0944.91003
[10] Y. Funaki, T. Yamato, Stable Coalition Structures Under Restricted Coalitional Changes, GLOPE working paper, Waseda University, 2010.; Y. Funaki, T. Yamato, Stable Coalition Structures Under Restricted Coalitional Changes, GLOPE working paper, Waseda University, 2010. · Zbl 1302.91015
[11] Gilboa, I.; Lehrer, E., Global games, International Journal of Game Theory, 20, 129-147 (1991) · Zbl 0743.90122
[12] Grabisch, M., The lattice of embedded subsets, Discrete Applied Mathematics, 158, 479-488 (2010) · Zbl 1186.91025
[13] Macho-Stadler, I.; Pérez-Castillo, D.; Wettstein, D., Sharing the surplus: an extension of the Shapley value for environments with externalities, Journal of Economic Theory, 135, 339-356 (2007) · Zbl 1186.91111
[14] Myerson, R. B., Values of games in partition function form, International Journal of Game Theory, 6, 23-31 (1977) · Zbl 0373.90091
[15] Ray, D.; Vohra, R., Equilibrium binding agreement, Journal of Economic Theory, 73, 30-78 (1997) · Zbl 0872.90125
[16] Thrall, R. M.; Lucas, W. F., \(n\)-Person games in partition function form, Naval Research Logistic Quarterly, 10, 281-298 (1963) · Zbl 0229.90056
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.