“Connection, Event Subscription, and the Strategic Formation of Networks” by Vai-Lam Mui
This paper presents a game-theoretic model of network formation, in which agents decide which events they will subscribe to, from a given set of events. The cost of subscribing to each event is exogenously given while the benefit derived by an agent from his subscription decisions depends on the structure of connections generated by the subscription decisions of all agents. In this environment, two agents are directly connected if they subscribe to at least one common event. Two agents who are not directly connected may be indirectly connected via agents who subscribe to multiple events and thereby serve as connectors. We first study a benchmark model with homogeneous agents and symmetric subscription costs. In this benchmark model, the efficient network involves either no one subscribing to any event or everyone subscribing to the same single event. We also determine the conditions under which the Nash equilibria of this network formation game are inefficient. We then extend the benchmark model to investigate how the results change when (1) the benefit derived by an agent from another agent is a function of the distance between them, (2) an event may fail because it only provides imperfectly reliable connections between subscribers, and (3) agents and/or events are heterogeneous. We determine the efficient network for each case, and show how benefit decay, imperfect reliability, and heterogeneity affect the conditions that will lead to the divergence between Nash stability and efficiency. We relate our two-mode network formation model that considers the role of both agents and events to the one-mode network formation literature pioneered by Jackson and Wolinsky (1996, Journal of Economic Theory), which does not consider the role of events.