Although both betweenness and closeness centrality are claimed to be important for the effectiveness of someone's network position, it has not been explicitly studied which networks emerge if actors follow incentives for these two positional advantages. We propose such a model and observe that network dynamics differ considerably in a scenario with either betweenness or closeness incentives compared to a scenario in which closeness and betweenness incentives are combined. Considering social consequences, we find low clustering when actors strive for either type of centrality. Surprisingly, actors striving for closeness are likely to reach networks with relatively low closeness and high betweenness, while this is the other way round for actors striving for betweenness. This shows that in both situations the network formation process implies a social dilemma in which the social optimum is not reached by individual optimizing.
Closeness centrality Betweenness centrality Actor utility Network dynamics Social dilemma