Group Formation with a Network Constraint

Group formation is an important part of many kinds of economic problems, including rent-seeking, resource management, contract bidding, volunteer organization, problem solving, and political lobbying. The current literature on group formation assumes that individuals are unconstrained in their choice of groups–that they may join any existing group. However, instances where group membership decisions are truly unconstrained are rare. Individuals face a wide range of social, geographic, and informational constraints in their group membership decisions. In this paper, I extend the existing group membership models to account for such widespread constraints. I imbed the players in a network of relationships, which constrains their choice of groups–they may only join a group if that group contains a member that they are connected to on the network. I then examine how this network constraint affects the equilibrium group structure. I show that when payoffs are single-peaked in group size and individuals are unconstrained in their group membership, they will form groups that are much too large, from the standpoint of social welfare. This is due to the externality that new members impose on the group’s existing membership–new members free ride off of the efforts of early group members, and new groups are under-provided. I then consider the effect of a network constraint on equilibrium group structure. I show that when individuals are constrained by their networks, the resulting group structures are much closer to the socially optimal group structure, and thus much more efficient. This is because the network constraint limits the ability of the individual to free ride on the efforts of other group members. The efficiency of the outcome is related to the structure of the network constraint–outcomes are more efficient when networks are sparse and have few random connections.