Socially Acceptable Values for Cooperative TU Games
Contributions to game theory and management, Tome 4 (2011), pp. 117-131.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the framework of the solution theory for cooperative transferable utility games, a value is called socially acceptable with reference to a certain basis of games if, for each relevant game, the payoff to any productive player covers the payoff to any non-productive player. Firstly, it is shown that two properties called desirability and monotonicity are sufficient to guarantee social acceptability of type $I$. Secondly, the main goal is to investigate and characterize the subclass of efficient, linear, and symmetric values that are socially acceptable for any of three types (with clear affinities to simple unanimity games).
Keywords: cooperative game, unanimity game, socially acceptable value, Shapley value, solidarity value, egalitarian value.
@article{CGTM_2011_4_a9,
     author = {Theo Driessen and Tadeusz Radzik},
     title = {Socially {Acceptable} {Values} for {Cooperative} {TU} {Games}},
     journal = {Contributions to game theory and management},
     pages = {117--131},
     publisher = {mathdoc},
     volume = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2011_4_a9/}
}
TY  - JOUR
AU  - Theo Driessen
AU  - Tadeusz Radzik
TI  - Socially Acceptable Values for Cooperative TU Games
JO  - Contributions to game theory and management
PY  - 2011
SP  - 117
EP  - 131
VL  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2011_4_a9/
LA  - en
ID  - CGTM_2011_4_a9
ER  - 
%0 Journal Article
%A Theo Driessen
%A Tadeusz Radzik
%T Socially Acceptable Values for Cooperative TU Games
%J Contributions to game theory and management
%D 2011
%P 117-131
%V 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2011_4_a9/
%G en
%F CGTM_2011_4_a9
Theo Driessen; Tadeusz Radzik. Socially Acceptable Values for Cooperative TU Games. Contributions to game theory and management, Tome 4 (2011), pp. 117-131. http://geodesic.mathdoc.fr/item/CGTM_2011_4_a9/

[1] Calvo E., “Random marginal and random removal values”, International Journal of Game Theory, 37 (2008), 533–563 | DOI | MR | Zbl

[2] Dragan I., Driessen T. S. H., Funaki Y., “Collinearity between the Shapley value and the egalitarian division rules for cooperative games”, OR Spektrum, 18 (1996), 97–105 | DOI | MR | Zbl

[3] Driessen T. S. H., Cooperative Games, Solutions, and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988 | Zbl

[4] Driessen T. S. H., Radzik T., “Extensions of Hart and Mas-Colell's consistency to efficient, linear, and symmetric values for TU-games”, ICM2002GTA proceedings volume of International Congress of Mathematicians, Game Theory and Applications Satellite Conference, eds. Gao H., Petrosjan L. A., Shao F. Jianpei, Xu J., Yeung D. W., Zakharov V. V., Zenkevich N. A., Z, Qingdao Publishing House, Qingdao,China, 2002, 129–146 | MR | Zbl

[5] Driessen T. S. H., Radzik T., “Extensions of Hart and Mas-Colell's consistency to efficient, linear, and symmetric values for TU-games”, ICM Millennium Lectures on Games, Volume dedicated to the International Congress of Mathematicians, Game Theory and Applications Satellite Conference (August 14–17, 2002, Qingdao, China), eds. Petrosyan L. A., Yeung D. W. K., Springer-Verlag, Heidelberg, Germany, 2003, 147–166 | DOI | MR

[6] Driessen T. S. H., Khmelnitskaya A. B., Sales J., “$1$-Concave basis for TU games and the library game”, TOP, Published online on 1st September 2010 | DOI | MR

[7] Hernández-Lamoneda L., Juárez R., Sánchez-Sánchez F., “Dissection of solutions in cooperative game theory using representation techniques”, International Journal of Game Theory, 35 (2007), 395–426 | DOI | MR | Zbl

[8] Joosten R., Peters`H. J. M., Thuijsman F., Socially acceptable values for transferable utility games, Report M94-03, Department of Mathematics, University of Maastricht, The Netherlands, 1994

[9] Nowak A. S., Radzik T., “A solidarity value for $n$-person transferable utility games”, International Journal of Game Theory, 23 (1994), 43–48 | DOI | MR | Zbl

[10] Nowak A. S., Radzik T., “On convex combinations of two values”, Applicationes Mathematicae, 24 (1996), 47–56 | MR | Zbl

[11] Roth A. E. (ed.), The Shapley value, Essays in honor of Lloyd S. Shapley, Cambridge University Press, Cambridge, U.S.A., 1988 | MR

[12] Ruiz L. M., Valenciano F., Zarzuelo J. M., “The family of least square values for transferable utility games”, Games and Economic Behavior, 24 (1998), 109–130 | DOI | MR | Zbl

[13] Shapley L. S., “A value for $n$-person games”, Annals of Mathematics Study, 28, Princeton University Press, 1953, 307–317 ; Also in [11] 31–40 | MR

[14] Schmeidler D., “The nucleolus of a characteristic function game”, SIAM Journal of Applied Mathematics, 17 (1969), 1163–1170 | DOI | MR | Zbl

[15] Tijs S. H., “Bounds for the core and the $\tau$-value”, Game Theory and Mathematical Economics, eds. Moeschlin O., Pallaschke D., North-Holland Publishing Company, Amsterdam, 1981, 123–132