A degree-distance-based connections model with negative and positive externalities

We develop a modification of the connections model by Jackson and Wolinsky (1996) that takes into account negative externalities arising from the connectivity of direct and indirect neighbors, thus combining aspects of the connections model and the co-author model. We consider a general functional form for agents’ utility that incorporates both the effects of distance and of neighbors’ degree. Consequently, we introduce a framework that can be seen as a degree-distance-based connections model with both negative and positive externalities. Our analysis shows how the introduction of negative externalities modifies certain results about stability and efficiency compared to the original connections model. In particular, we see the emergence of new stable structures, such as a star with links between peripheral nodes. We also identify structures, for example, certain disconnected networks, that are efficient in our model but which could not be efficient in the original connections model. While our results are proved for the general utility function, some of them are illustrated by using a specific functional form of the degree-distance-based utility.