Network Formation with Closeness Incentives

Closeness centrality is an index that has been widely used to assess the strength of an agent's position in a network of relationships. We study the formation of networks in a strategic setting, where every agent tries to optimize his closeness centrality. We investigate how the curvature of the benefit function (decreasing vs. increasing marginal returns) affects the set of stable networks and compare the results to the well-known connections model of Jackson and Wolinsky (JET 71, 1996). It turns out that our model can “replicate” the connections model in the sense that each result is translatable from one model into the other and the sets of stable networks coincide for certain specifications. We conclude that the two models incorporate the same kind of linking behavior and that grouping these “closeness-type” models means a first step in organizing network formation models by the type of incentives.