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.

Figure 1

An example run for a 200-agent system with $p_r=0.012$. (a) and (b) show the fraction of vertices having a certain leading strategy for addition (a) and deletion (b), respectively. (c) shows the average score, (d) the average degree, and (e) the relative size of the largest connected component.

Figure 2

The network structure with MAXC as the leading addition action. Parameter values are the same as in Fig. 1. Panel (a) shows the degree distribution for time steps where more than a half of the agents use MAXC as leading action. The curves are log-binned for large degrees. Errors are smaller than the symbol size. Panel (b) shows an example graph for $N=200$. We emphasize that this is only one of a great variety on network topologies that emerge from the dynamics. The colors of the vertices represent the addition actions as in Fig. 1.

Figure 3

The system’s dependence on the fraction of random rewirings $p_r$ and system size $N$. Panels (a), (b), and (c) show the fraction of preferred addition actions $⟨{\sigma }_1^{\mathrm{add}}⟩$ for systems of 200, 400, and 800 agents, respectively. Panels (d), (e), and (f) show the fraction of preferred deletion actions for the same three system sizes, while (g) shows the average degree and (h) the average relative size of the largest connected component.