Group identity in a network formation game with cost sharing

This paper introduces the choice of group identity, which is comprised of characteristics and commitments to these characteristics, in a network formation model where links costs are shared. Players want to link to the largest group given that linking costs for players of the same (different) characteristic are decreasing (increasing) in their commitments. The equilibrium concepts used are Nash equilibrium as well as one that looks for stability allowing for bilateral negotiations. Conditions are shown under which the endogenous choice of characteristics and commitments allow for multiple groups with segregated or connected networks. When group identity is partly endogenous, such that characteristics are fixed and players only choose commitment, it is shown that the equilibrium population commitment profile dictates whether the resulting network is segregated or connected. When group identity is fully endogenous, it is shown that multiple groups and segregated networks are possible equilibrium outcomes but such outcomes are not stable unless the group size additionally affects the costs of link formation.