Geodesic
One axiomatization of generalized Owen extension
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 1 (2009) no. 2, pp. 3-13.

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

New approach to generalized Owen extension's construction for some classes of polynomial games is considered. It is proved that this extension coincides with Aumann-Shapley extension for one class of nonatomic games. The explicit formula for multiplicative Aumann-Shapley extension is obtained. The axiomatization of classical Owen extension for the class of discrete-time cooperative games is obtained and it differs from Aumann-Shapley axiomatization only by weak multiplicative axiom.
Keywords: cooperative games, polynomial games, Owen extension, Aumann-Shapley extension. 
@article{MGTA_2009_1_2_a0,
     author = {Valeri Vasil'ev},
     title = {One axiomatization of generalized {Owen} extension},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {3--13},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2009_1_2_a0/}
}
TY  - JOUR
AU  - Valeri Vasil'ev
TI  - One axiomatization of generalized Owen extension
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2009
SP  - 3
EP  - 13
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2009_1_2_a0/
LA  - ru
ID  - MGTA_2009_1_2_a0
ER  - 
%0 Journal Article
%A Valeri Vasil'ev
%T One axiomatization of generalized Owen extension
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2009
%P 3-13
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2009_1_2_a0/
%G ru
%F MGTA_2009_1_2_a0
Valeri Vasil'ev. One axiomatization of generalized Owen extension. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 1 (2009) no. 2, pp. 3-13. http://geodesic.mathdoc.fr/item/MGTA_2009_1_2_a0/

[1] R. Auman, L. Shepli, Znacheniya dlya neatomicheskikh igr, Mir, Moskva, 1977 | MR

[2] V.A. Vasilev, “Obschaya kharakteristika polinomialnykh funktsii mnozhestva”, Optimizatsiya, 14 (1974), 103–123 | Zbl

[3] J.A. Harsanyi, “A bargaining model for cooperative $n$-person games”, Contributions to the Theory of Games, v. IV, eds. A.W. Tucker and R.D. Luce, 1959, 325–355 | MR | Zbl

[4] G. Owen, “Multilinear extensions of games”, Journal of Management Sciences, 18:5 (1972), 64–79 | DOI | MR | Zbl

[5] V.A. Vasil'ev, “The Shapley functional and the polar form of homogeneous polynomial games”, Siberian Advances in Mathematics, 8:4 (1998), 109–150 | MR | Zbl

[6] V.A. Vasil'ev, “Polar forms, $p$-values, and the core”, Approximation, Optimisation and Mathematical Economics, ed. M. Lassonde, Physica-Verlag, Heidelberg-New York, 2001, 357–368 | DOI | MR | Zbl

[7] V.A. Vasil'ev, “Cores and generalized NM-solutions for some classes of cooperative games”, Russian Contributions to Game Theory and Equilibrium Theory, eds. T. Driessen, G. van der Laan, V. Vasil'ev, and E. Yanovskaya, Springer-Verlag, Berlin-Heidelberg-New York, 2006, 91–150 | DOI