We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network.
Competitive Dynamics on Complex Networks
Jiuhua Zhao, Qipeng Liu, & Xiaofan Wang
Scientific Reports 4, Article number: 5858
Via Complexity Digest, Jocelyn Stoller