Under-connected and over-connected networks: the role of externalities in strategic network formation

Abstract

Since the seminal contribution of Jackson and Wolinsky (J Econ Theory 71(1): 1996) it has been widely acknowledged that the formation of social networks exhibits a general conflict between individual strategic behavior and collective outcome. What has not been studied systematically are the sources of inefficiency. We approach this omission by analyzing the role of positive and negative externalities of link formation. This yields general results that relate situations of positive externalities with stable networks that cannot be "too dense" in a well-defined sense, while situations with negative externalities tend to induce "too dense" networks. Those results are neither restricted to specific assumptions on the agents' preferences (e.g. homogeneity), nor to a specific notion of stability or efficiency.

Network Formation with Local Complements and Global Substitutes: The Case of R&D Networks

“…It illustrates the region of inefficiency of the equilibrium network for linking costs ζ < ζ * , where equilibrium networks typically tend to be under-connected [cf. Buechel and Hellmann, 2012]. 33 As similar observation can also be made for heterogeneous firms considered in part (ii) of Proposition 4.…”

“…We then investigate the efficient network and output structure that maximize social welfare, and find that equilibrium networks tend to be under-connected [cf. Buechel and Hellmann, 2012], compared to the social optimum. 4 Second, we bring the model to the data by analyzing a unique dataset of firm R&D collaborations matched to firms' balance sheets.…”

A Degree‐Distance‐Based Connections Model with Negative and Positive Externalities

“…The conditions required in our proof are quite restrictive but compatible with the stability of the star structures with peripheral links. Thus, our model can indeed generate overconnectedness as defined by Buechel and Hellmann (), which could never occur in the original connections model.…”

“…The result about the efficiency of the star also shows that the efficient network can be strictly contained in a (or the, in the case of uniqueness) pairwise stable network. This implies that our model can give rise to overconnectivity in the strong sense defined by Buechel and Hellmann (), which could never occur in the original connections model.…”

A Degree-Distance-Based Connections Model with Negative and Positive Externalities

“…As shown in Jackson and Wolinsky (1996) strongly efficient networks may not be stable, and conversely networks need not be efficient even when they are uniquely stable. Buechel and Hellmann (2012) show that inefficient outcomes can be related to the nature of the externalities. They introduce the notion of overconnected (underconnected) networks-those which can be socially improved by the deletion (addition) of links.…”