Unequal connections

Empirical work suggests that social and economic networks are characterized by an unequal distribution of connections across individuals. This paper explores the circumstances under which networks will or will not exhibit inequality. Two specific models of network formation are explored. The first is a playing the field game in which the aggregate payoffs of an individual depend only on the number of his links and the aggregate number of links of the rest of the population. The second is a local spillovers game in which the aggregate payoffs of an individual depend on the distribution of links of all players and the identity of neighbors. For both class of games we develop results on existence and characterize equilibrium networks under different combinations of externalities/spillovers. We also examine conditions under which having more connections implies a higher payoff.