Eight degrees of separation

We present a network formation game whose equilibria are undirected networks. Every connected couple contributes to the aggregate payoff by a fixed quantity, and the outcome is split between players according to the Myerson value allocation rule. This setup shows a wide multiplicity of non-empty equilibria, all of them connected.Weshow that the efficient equilibria of the game are either the empty network, or a network whose diameter does not exceed a threshold of 8 (i.e. there are no two nodes with a distance greater than 8).