This article is devoted to cooperative network games with pairwise interaction. We consider a two-stage game, the first stage of which represents a network-formation stage, and the second is simultaneous bimatrix games, which take place between neighbours over the network. The characteristic function is constructed, its supermodularity is proved for the case of a one-step subgame starting with the second stage. For a special class of networks (star-network), a simplified formula for the Shapley vector is found, which does not require the calculation of the values of the characteristic function over all coalitions, but only over coalitions of dimension no more than two.