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

Working paper

Issue number:

2013.40

Publisher:

Centre d’Economie de la Sorbonne

Year:

2013

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.