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Closeness is a global measure of centrality in networks, and a proxy for howinfluential actors are in social networks. In most network models, and manyempirical networks, closeness is strongly correlated with degree. However, insocial networks there is a cost of maintaining social ties. This leads to asituation (that can occur in the professional social networks of executives,lobbyists, diplomats and so on) where agents have the conflicting objectives ofaiming for centrality while simultaneously keeping the degree low. Weinvestigate this situation in an adaptive network-evolution model where agentsoptimize their positions in the network following individual strategies, andusing only local information. The strategies are also optimized, based on thesuccess of the agent and its neighbors. We measure and describe the timeevolution of the network and the agents' strategies.

The diplomat's dilemma: Maximal power for minimal effort in social networks