Dynamics of networking agents competing for high centrality and low   degree
  We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution, the success of the agents is related only to their position in the network. The agents use strategies based on local information to improve their chance of success. Both the evolution of strategies and network structure are investigated. We find a dramatic time evolution with cascades of strategy change accompanied by a change in network structure. On average the network self-organizes to a state close to the transition between a fragmented state and a state with a giant component. Furthermore, with increasing system size both the average degree and the level of fragmentation decreases. We also observe that the network keeps on actively evolving, although it does not have to, thus suggesting a Red Queen-like situation where agents have to keep on networking and responding to the moves of the others in order to stay successful. 
Petter Holme and Gourab Ghoshal