Recalibrating influence propagation for competitive independent cascade

In competitive influence propagation problems, users are often exposed to multiple competing influences, and their likelihood of accepting these influences is affected by the frequency of exposure, rather than being equally distributed as assumed in traditional models like the Competitive Independent Cascade (CIC) model. The CIC model, while useful, simplifies the decision-making process by treating each influence as equally probable. However, in reality, individuals tend to favor the influence they encounter more frequently, a phenomenon driven by Herd Mentality. To address this limitation, we propose an enhanced influence propagation model that incorporates the frequency of received information to more accurately reflect real-world decision-making. By considering the frequency with which each influence is encountered, we modify the original model to calculate a more realistic propagation scale, $$\sigma (\cdot )$$ σ ( · ) . This new model records the incentive values associated with each influence and tracks the activation times of users across the network. Through both theoretical analysis and experimental validation, we demonstrate that our model produces significantly different results from the original CIC model, highlighting the importance of considering the frequency of influence reception in competitive environments. The experimental findings confirm that our frequency-based approach provides most different prediction results of influence spread in practical scenarios comparing with the CIC model.