Social Clubs and Social Networks

Abstract: We present a strategic network formation model which is based on club memberships. Agents choose the set of clubs with which they wish to be affiliated. The set of all club memberships (an Environment) induces a weighted social network where two agents are directly connected if they share a club. Two agents may also be indirectly connected using multiple memberships of third parties. Thus, the clubs and the network are formed simultaneously. Using this setting of club affiliation we introduce two models – one of club congestion where each link’s weight depends on the original club size, and one of individual congestion where each link’s weight depends on the number of affiliations of both agents. We introduce several stability concepts interpreted as different sets of club rules. For each model, we demonstrate the main trade-offs and characterize the environments that may emerge. In particular, in the club congestion model we focus on the trade-off between the club’s size and the indirect connections’ depreciation while in the individual congestion model a coordination failure may arise due to the externalities incurred by the formation of a new club. We show that clubs’ rules and deviations complexity are crucial in determining the set of stable environments.