The Formation of Networks with Side Payments

We examine the formation of networks among a set of players whose payoffs depend on the structure of the network. We focus on games where players may promise or demand transfer payments when forming links. If players may only make such transfers on the links they are directly involved with, then there are many settings where inefficient networks are the only equilibrium outcomes, and we fully characterize the supportable networks. If externalities are nonpositive and a convexity condition is satisfied, then efficient networks are supportable as equilibria with such direct transfers. If players can also make positive transfers to pay for links they are not involved with, then a convexity condition alone is sufficient for an efficient network to be supportable as an equilibrium. In cases where transfers can be made contingent on the network, then any efficient network is supportable as an equilibrium. We also consider a refinement of equilibrium that allows pairs of players to coordinate their promises and demands on a link. If players can make payments to prevent the formation of a link as well as to form it, then all efficient networks are supportable via the pairwise equilibrium refinement