Sufficient Conditions for Formation of a Network Topology by Self-interested Agents by Swapnil Dhamal and Y. Narahari.
Abstract:
The current literature on network formation primarily addresses the problem: given a set of self-interested nodes and a set of conditions, what topologies are pairwise stable and hence are likely to emerge. A pairwise stable network is one in which no node wants to delete any of its links and no two nodes would want to create a link between them. Pairwise stable networks span a wide range of topologies and some of them might be far from desirable. Motivated by the necessity for ensuring that the emerging network is exactly a desired one, we study the following reverse problem: given a network topology, what conditions are required so that best response strategies played by self-interested agents ultimately result in that network topology. We propose a sequential network formation game model that captures principal determinants of network formation, namely benefits from immediate neighbors, costs of maintaining links with immediate neighbors, benefits from indirect neighbors, and bridging benefits. Based on this model, we analyze some common network topologies, namely star, complete graph and bipartite Turán graph, and derive a set of sufficient conditions under which these network topologies emerge.
I mention this to suggest that as future work, merging of nodes based on the subject they represent should be considered as a benefit. Depending upon linking, merger could result in a reduction of linking between nodes, something the authors already recognize as a potential benefit. The potential exists for some merging operations to be found to be too expensive, either temporarily or longer term.
Rather than an axiomatic merging rule, a cost/benefit merging rule that is invoked only in some circumstances.