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

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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/}
}
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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/