Geodesic
Non-zero sum network games with pairwise interactions
Contributions to game theory and management, Tome 14 (2021), pp. 38-48.

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

In the paper non-zero sum games on networks with pairwise interactions are investigated. The first stage is network formation stage, where players chose their preferable set of neighbours. In all following stages simultaneous non-zero sum game appears between connected players in network. As cooperative solutions the Shapley value and $\tau$-value are considered. Due to a construction of characteristic function both formulas are simplified. It is proved, that the coefficient $\lambda$ in $\tau$-value is independent from network form and number of players or neighbours and is equal to $\frac{1}{2}$. Also it is proved that in this type of games on complete network the Shapley value and $\tau$-value are coincide.
Keywords: cooperative games, network games, dynamic games, the Shapley value, $\tau$-value. 
@article{CGTM_2021_14_a3,
     author = {Mariia A. Bulgakova},
     title = {Non-zero sum network games with pairwise interactions},
     journal = {Contributions to game theory and management},
     pages = {38--48},
     publisher = {mathdoc},
     volume = {14},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2021_14_a3/}
}
TY  - JOUR
AU  - Mariia A. Bulgakova
TI  - Non-zero sum network games with pairwise interactions
JO  - Contributions to game theory and management
PY  - 2021
SP  - 38
EP  - 48
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2021_14_a3/
LA  - en
ID  - CGTM_2021_14_a3
ER  - 
%0 Journal Article
%A Mariia A. Bulgakova
%T Non-zero sum network games with pairwise interactions
%J Contributions to game theory and management
%D 2021
%P 38-48
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2021_14_a3/
%G en
%F CGTM_2021_14_a3
Mariia A. Bulgakova. Non-zero sum network games with pairwise interactions. Contributions to game theory and management, Tome 14 (2021), pp. 38-48. http://geodesic.mathdoc.fr/item/CGTM_2021_14_a3/

[1] Tijs S. H., “An axiomatization of the $\hat{o}$-value”, Mathematical Social Sciences, 13 (1987), 177–181 | MR | Zbl

[2] Dyer M., V. Mohanaraj, “Pairwise-Interaction Games”, ICALP: Automata, Languages and Programming, 2011, 159–170 | MR | Zbl

[3] Shapley L. S., “A value for $n$-person games”, Contributions to the theory of games II, eds. H. W. Kuhn, A. W. Tucker, Princeton, 1953, 307–317 | MR

[4] Bulgakova M. A., L. A. Petrosyan, “Cooperative network games with pairwise interactions”, Mathematical game theory and applications, 4:7 (2015), 7–18 | MR | Zbl

[5] Bulgakova M. A., “Solutions of network games with pairwise interactions”, Vestnik of Saint-Petersburg State university. Series 10. Applied mathematics. Informatics. Control processes, 15:1 (2019), 147–156 | MR

[6] Bulgakova M. A., “About one multistage non-zero sum game on the network”, Vestnik of Saint-Petersburg State university. Series 10. Applied mathematics. Informatics. Control processes, 15:4 (2019), 603–615 | MR

[7] Petrosyan L. A., N. N. Danilov, “Stability of solutions of non-zero-sum game with transferable payoffs”, Vestnik of the Leningrad University. Series 1. Mathematics. Mechanicks. Astronomy, 1 (1979), 52–59 | MR | Zbl