Network extension

Abstract

a b s t r a c tIn a model of strategic network formation, the endogenously formed network is built around a preexisting network. We envisage that the pre-existing or core network is publicly provided. Strategic network formation is decentralized: Players act in their private interest and bear the costs when adding links to the pre-existing network. We study how the pre-existing network affects existence of Nash equilibria and efficiency of Nash equilibrium outcomes: It can foster or prohibit existence of Nash equilibria. It can improve or worsen equilibrium welfare. Special attention is paid to an insider-outsider model where society is partitioned into several groups and links within a group (between insiders) are much cheaper than links across groups (between outsiders). We also present equilibrium existence results and examine the effect of Pareto optimal publicly provided networks.

Constrained Network Formation

“…4 Analogously, the following result, related to networks of positive constraints which are (in the unconstrained model of network formation) Pareto optimal, generalises Proposition 2 by Haller (2012).…”

“…2 It can be easily verified that when g − = e, this coincides with the payoff function defined by Haller (2012). With all the components of the model exposed, we can proceed to the generalisation of some of his results concerning Nash networksthat is, networks which are stable with respect to individual deviations.…”

“…Like the original proof by Haller (2012), it relies on the observation that the proof of existence by Haller et al (2007) does not exploit the homogeneity of costs, only the owner-homogeneity.…”

“…The case g − = e is Proposition 2 by Haller (2012). When considering g − = e, the actions set of some nodes is restricted, but the links in g + are left untouched (recall that g + and g − are disjoint).…”

“…3. Only recently some form of constrained growth was formalised in the context of strategic network formation by Haller (2012). His study provides interesting conclusions concerning networks which grow around an exogenously fixed subset of links, shown to potentially change drastically the existence, numerosity, stability and efficiency of stable configurations.…”