Social Clubs and Social Networks

We present a strategic network formation model which is based on membership in clubs. Agents choose a set of clubs with which they wish to be affiliated. The set of all club memberships (an environment) induces a weighted network in which two agents are directly connected if they are members of the same club. Two agents may also be indirectly connected using the multiple memberships of third parties. Agents gain from their position in the induced network and pay membership fees. Thus, both clubs and the network are formed simultaneously. Using two specifications of the weighting function we introduce two models based upon congestion - one, the club congestion model wherein the weight of each link depends upon the size of the smallest shared club and the other, the individual congestion model wherein each link's weight depends on the number of affiliations maintained by the two agents. In the club congestion model we focus on the trade-off between the size of the club, depreciation due to indirect connections and membership fees. In the individual congestion model the Grand Club environment is the unique efficient environment. However, a coordination failure arises due to the wide externalities incurred by the formation of new affiliations. We believe that this framework may serve as a basis for an empirical examination of the role of linking platforms in shaping real-life social networks.