Geodesic
The joint axiomatization of the prenucleolus and the Dutta-Ray solution for convex games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 2, pp. 96-123.

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

Most of cooperative TU game solutions are covariant with respect to positive linear transformations of individual utilities. However, this property does not take into account interpersonal comparisons of players' payoffs. The constrained egalitarian solution defined by Dutta and Ray [4] for the class of convex TU games, being not covariant, served as a pretext to studying non-covariant solutions. In the paper a weakening of covariance is given in such a manner that, together with some other properties, it characterizes only two solutions – the prenucleolus and the Dutta–Ray solution – on the class of convex TU games.
Keywords: cooperative game, restricted cooperation, prenucleolus
Mots-clés : coalitional structure. 
@article{MGTA_2012_4_2_a5,
     author = {Elena B. Yanovskaya},
     title = {The joint axiomatization of the prenucleolus and the {Dutta-Ray} solution for convex games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {96--123},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2012_4_2_a5/}
}
TY  - JOUR
AU  - Elena B. Yanovskaya
TI  - The joint axiomatization of the prenucleolus and the Dutta-Ray solution for convex games
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2012
SP  - 96
EP  - 123
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2012_4_2_a5/
LA  - ru
ID  - MGTA_2012_4_2_a5
ER  - 
%0 Journal Article
%A Elena B. Yanovskaya
%T The joint axiomatization of the prenucleolus and the Dutta-Ray solution for convex games
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2012
%P 96-123
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2012_4_2_a5/
%G ru
%F MGTA_2012_4_2_a5
Elena B. Yanovskaya. The joint axiomatization of the prenucleolus and the Dutta-Ray solution for convex games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 2, pp. 96-123. http://geodesic.mathdoc.fr/item/MGTA_2012_4_2_a5/

[1] Sobolev A. I., “Kharakterizatsiya printsipov optimalnosti v kooperativnykh igrakh posredstvom funktsionalnykh uravnenii”, Matematicheskie metody v sotsialnykh naukakh, 6, In-t matematiki i kibernetiki AN Lit SSR, Vilnyus, 1975, 94–151 | Zbl

[2] Davis M., Maschler M., “The kernel of a cooperative game”, Naval Research Logistics Quarterly, 12 (1965), 223–259 | DOI | MR | Zbl

[3] Dutta B., “The egalitarian solution and the reduced game properties in convex games”, International Journal of Game Theory, 19 (1990), 153–159 | DOI | MR

[4] Dutta B., Ray D., “A concept of egalitarianism under participation constraint”, Econometrica, 51 (1989), 615–635 | DOI | MR

[5] Hart S., Mas-Colell A., “Potential, value, and consistency”, Econometrica, 57 (1989), 589–614 | DOI | MR | Zbl

[6] Hokari T., “Population monotonic solutions on convex games”, International Journal of Game Theory, 29 (2000), 327–338 | DOI | MR | Zbl

[7] Maschler M., “The bargaining set, kernel, and nucleolus”, Handbook of Game Theory with Economic Applications, v. I, Handbooks in Economics, 11, eds. R. J. Aumann, S. Hart, Elsevier Science Publishers, Amsterdam, The Netherlands, 1992, 591–667 | MR | Zbl

[8] Moulin H., Axioms of cooperative decision making, Econometric Society Monographs, 15, Cambridge University Press, Cambridge, 1988 | MR | Zbl

[9] Moulin H., “Axiomatic cost and surplus sharing methods”, Handbook on Social Choice and Welfare, 2001, 289–360

[10] Rosenthal E. C., “Monotonicity of the core and value in dynamic cooperative games”, International Journal of Game Theory, 19 (1990), 45–57 | DOI | MR | Zbl

[11] Shapley L. S., “A value for $n$-person games”, Annals of Mathematics Study, 28 (1953), 307–317 | MR | Zbl

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

[13] Sprumont Y., “Population monotonic allocation schemes for cooperative games with transferable utility”, Games and Economics Behavior, 2 (1990), 378–394 | DOI | MR | Zbl

[14] Thomson L., “Cooperative models of Bargaining”, Handbook of game theory with economic applications, Handbooks in Economics, 11, eds. R. J. Aumann, S. Hart, Elsevier Science Publishers, Amsterdam, The Netherlands, 1994, 1237–1284 | MR