Eight Degrees of Separation

Abstract

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 the threshold of 8 (i.e. there are no two nodes with distance greater than 8).