In a model of strategic network formation, the endogenously formed network is built around a pre-existing 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.
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