Non-Zero Sum Network Games with Pairwise Interactions

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 τ -value are considered. Due to a construction of characteristic function both formulas are simpli ed. It is proved, that the coeffcient λ in τ -value is independent from network form and number of players or neighbours and is equal to 1/2 . Also it is proved that in this type of games on complete network the Shapley value and τ -value are coincide.

The τ-value in Multistage Games with Pairwise Interactions

“…In (Bulgakova, 2021) we get, that the coefficient λ for τ -value in two-stage game with pairwise interactions Γ S z1 (g) is equal to 1 2 and the formula for τ -value has form…”

“…This principle implies splitting the game into a family of simultaneous games between pairs of players -the vertices of the same edge in the network. In (Bulgakova, 2021) the Shapley value for two-stage game with pairwise interactions was found. Two-stage network games and the mechanism of network formation also was considered in (Petrosyan et al, 2013).…”