Network formation under negative degree-based externalities

While a relationship in a social or business network should be mutually beneficial, it is ambiguous whether the relationship benefits or harms the rest of the network. This paper focuses on the situation where any new relationship imposes a negative externality on the rest of the network. We model this by assuming an agent’s payoff from a relationship is a decreasing function of the number of relationships the other agent maintains. We solve for the socially efficient and stable networks. While in general the two diverge, we demonstrate that they coincide when agents are able to make transfers to their partners.