No 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.

This article is an overview of results obtained in the field of dynamic network games with pairwise interaction. The paper provides a summary and analysis of works related to two-stage and multistage nonzero-sum games based on pairwise interaction. The meaning of pairwise interaction is to consider the game as a family of games occurring on a network between pairs of players (vertices of a graph) connected to each other by an edge. The network can be set or formed in the first stage. In the paper, solutions of cooperative pairwise interaction games are also considered.

We consider multistage bimatrix games with pairwise interactions. On the first stage players chose their neighbours and formed a network. On the later stages bimatrix games between neighbours by network take places. As a solution consider the τ-value (Tijs, 1987). Earlier we calculated coefficient λ of τ-value in case of two-stage game. Now we consider a general case of one-stage game with any players and any number of links. We assumed followings: N is set of players, N ≥ 2 and any type of network g. It is also assumed, that there are not necessarily paths between every pair of vertices. We will consider conditions for time-consistency of τ-value in two-stage game.