Geodesic
Solutions of network games with pairwise interactions
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 1, pp. 147-156 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This article is devoted to cooperative network games with pairwise interaction. We consider a two-stage game, the first stage of which represents a network-formation stage, and the second is simultaneous bimatrix games, which take place between neighbours over the network. The characteristic function is constructed, its supermodularity is proved for the case of a one-step subgame starting with the second stage. For a special class of networks (star-network), a simplified formula for the Shapley vector is found, which does not require the calculation of the values of the characteristic function over all coalitions, but only over coalitions of dimension no more than two.
Keywords: cooperative games, convexity, Shapley value, characteristic function. 
@article{VSPUI_2019_15_1_a11,
     author = {M. A. Bulgakova},
     title = {Solutions of network games with pairwise interactions},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {147--156},
     year = {2019},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2019_15_1_a11/}
}
TY  - JOUR
AU  - M. A. Bulgakova
TI  - Solutions of network games with pairwise interactions
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2019
SP  - 147
EP  - 156
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2019_15_1_a11/
LA  - ru
ID  - VSPUI_2019_15_1_a11
ER  - 
%0 Journal Article
%A M. A. Bulgakova
%T Solutions of network games with pairwise interactions
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2019
%P 147-156
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/VSPUI_2019_15_1_a11/
%G ru
%F VSPUI_2019_15_1_a11
M. A. Bulgakova. Solutions of network games with pairwise interactions. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 1, pp. 147-156. http://geodesic.mathdoc.fr/item/VSPUI_2019_15_1_a11/

[1] Dyer M., Mohanaraj V., “Pairwise-interaction games”, ICALP, v. 1, 2011, 159–170 | MR | Zbl

[2] Acemoglua D., Ozdaglarb A., Parandeh Gheibib A., “Spread of (mis)information in social networks”, Games and Economic Behavior, 70:2 (2010), 194–227 | DOI | MR

[3] König M. D., Battistonb S., Napoletanoc M., Schweitzerb F., “The efficiency and stability of R$\, \ \,$D networks”, Games and Economic Behavior, 75:2 (2012), 694–713 | DOI | MR | Zbl

[4] Petrosyan L. A., Sedakov A. A., “Multistage network games with full information”, Mathematical game theory and applications, 1:2 (2009), 66–81 (In Russian) | Zbl

[5] Bulgakova M. A., Petrosyan L. A., “About strongly time-consistency of core in the network game with pairwise interactions”, Proceedings of 2016 Intern. Conference “Stability and Oscillations of Nonlinear Control Systems”, 2016, 157–160

[6] Kuzyutin D., Nikitina M., “Time consistent cooperative solutions for multistage games with vector payoffs”, Operations Research Letters, 45:3 (2017), 269–274 | DOI | MR | Zbl

[7] Shapley L. S., “Cores of convex games”, Intern. Journal of Game Theory, 1 (1971), 11–26 | DOI | MR | Zbl

[8] Shapley L. S., “A value for $n$-person games”, Contributions to the theory of games, v. II, Annals of Mathematical Studies, 28, eds. H. W. Kuhn, A. W. Tucker, Princeton University Press, Princeton, 1953, 307–317 | MR

[9] Petrosyan L., Bulgakova M., Sedakov A., “Time-consistent solutions for two-stage network games with pairwise interactions”, Game Theory for Networking Applications, 2018, 15–23