Abstract:
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.
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