Competition between two sets of agents on complex networks

In this paper, we consider the competitive dynamics on complex networks where two sets of agents have fixed and opposite-signed states, called competitors, and other agents, called normal agents, update their states based on the influence of their neighbors. The competition outcome is defined in terms of the number of normal agents with specific sign. We introduce a criterion based on the Influence Matrix (IM), which is constructed according to the structure of the network, to predict the bias of each normal agent and furthermore predict which set of competitors will win the competition. We also compare the performance of IM criterion with several classic centrality-based criteria in predicting the competition outcome. Simulations show that, in the aspect of predicting the bias of a normal agent, the average success rate of IM criterion keeps high as the cardinality of set of competitors varies. In predicting the result of the competition, for undirected networks, IM criterion performs better than other centrality based criteria when the cardinality of the set of competitors is greater than one. For directed networks, IM criterion is also one of the best criteria.