The formation of networks with transfers among players

We examine the formation of networks among a set of players whose payoffs depend on the structure of the network, when players may bargain by promising or demanding transfer payments when forming links. We vary three aspects of the game: (i) whether players can only make transfers to (and receive transfers from) players to whom they are directly linked, or whether they can also subsidize links that they are not directly involved in, (ii) whether or not transfers relating to a given link can be made contingent on the full resulting network or only on the link itself, and (iii) whether or not players can pay other players to refrain from forming links. We characterize the networks that are supported under these variations and show how each of the above aspects either accounts for a specific type of externality, or deals with the combinatorial nature of network payoffs.