Potential maximizers and network formation

In this paper we study the formation of cooperation structures in superadditive cooperative TU-games. Cooperation structures are represented by hypergraphs. The formation process is modelled as a game in strategic form, where the payoffs are determined according to a weighted (extended) Myerson value. This class of solution concepts is the unique class resulting in weighted potential games. The argmax set of the weighted potential predicts the formation of the complete structure and structures payoff-equivalent to the complete structure. As by-products we obtain a representation theorem of weighted potential games in terms of weighted Shapley values and a characterization of the weighted (extended) Myerson values.