Bridging Network Gaps Under Limited Perception

We consider a model of network formation in which agents benefit from intermediation insofar as they are the only bridge between agents who would otherwise be unconnected. Their payoffs depend proportionally on their frequency as intermediaries. We analyze two types of payoffs: global, based on the intermediation across the whole network; and local, based on an agent’s perceived centrality in a subnetwork, measured within a fixed radius around the agent. These capture two measurements of network importance: objective and perceived (subjective). Agents have an incentive to form links so that they become key intermediaries in their (perceived) network and to bypass other key intermediaries in it. However, because payoffs are determined relative to other agents’ contributions, an agent might refrain from forming links if this would expose them to relatively more essential players. In case agents’ payoffs are global, the pairwise stable networks are connected and have at most one (central) agent with a nonzero payoff. In the case where agents’ payoffs are local, we describe the pairwise stable networks and some characteristics of the individual payoffs within them. A class of networks we call augmented stars (stars in which spokes may be connected but no cycle encompasses all spokes) is pairwise stable for both global and all possible local payoffs.