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. We show 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).

Research highlights
► A network formation game whose equilibria are undirected networks.
► Every connected couple contributes to the aggregate payoff by a fixed quantity.
► The outcome is split between players according to the Myerson value allocation rule.
► This setup shows wide multiplicity of non-empty equilibria, all of them connected.
► The diameter of the efficient equilibria does not exceed a threshold of 8.