Geodesic
Formation of new structure of coalitions in voting games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 1, pp. 61-73 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The new $(n+1)$st player enters the voting game and buys the stock from another players, investing the vector $\alpha=(\alpha_1,\dots,\alpha_n)$: $\sum_{i=1}^n\alpha_{i}\leq M$, $\alpha_i\geq0$, $\forall i=1,\dots,n$. The optimal investment is defined as $\alpha^*$, which maximizes the component of Shapley–Shubik value of entering player. The mathematical statement of the problem is given, some properties of the optimal investment are considered and Monte-Karlo method for the calculation of optimal investment is proposed.
Keywords: voting game, Shapley–Shubic value, profitable investment, veto-player, Monte-Karlo method.
Mots-clés : perspective coalitions 
@article{MGTA_2013_5_1_a3,
     author = {Ovanes L. Petrosian},
     title = {Formation of new structure of coalitions in voting games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {61--73},
     year = {2013},
     volume = {5},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2013_5_1_a3/}
}
TY  - JOUR
AU  - Ovanes L. Petrosian
TI  - Formation of new structure of coalitions in voting games
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2013
SP  - 61
EP  - 73
VL  - 5
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MGTA_2013_5_1_a3/
LA  - ru
ID  - MGTA_2013_5_1_a3
ER  - 
%0 Journal Article
%A Ovanes L. Petrosian
%T Formation of new structure of coalitions in voting games
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2013
%P 61-73
%V 5
%N 1
%U http://geodesic.mathdoc.fr/item/MGTA_2013_5_1_a3/
%G ru
%F MGTA_2013_5_1_a3
Ovanes L. Petrosian. Formation of new structure of coalitions in voting games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 1, pp. 61-73. http://geodesic.mathdoc.fr/item/MGTA_2013_5_1_a3/

[1] Petrosyan L. A., Zenkevich N. A., Shevkoplyas E. V., Teoriya Igr, BKhV-Peterburg, Sankt-Peterburg, 2012

[2] Hu X., “An asymmetric Shapley–Shubik power index”, International Journal of Game Theory, 34:1 (2006), 229–240 | MR | Zbl

[3] Shapley L. S., Shubik M., “A Method for Evaluating the Distribution of Power in a Committee System”, American Political Science Review, 48:3 (1954), 787–792 | DOI

[4] Shapley L. S., Shubik M., “On market games”, Journal of Economic Theory, 1:1 (1969), 9–25 | DOI | MR