Will the Winner Take All? Competing Influences in Social Networks Under Information Overload

Competitive influence diffusion occurs in settings ranging from product competition to online information propagation. Classical models often predict winner-takes-all outcomes, whereas persistent coexistence is observed in practice. We revisit this discrepancy by jointly considering incomplete network observation and information overload. An isotropic-Gaussian surrogate for a network embedding enables tractable mean-field estimation of overload timing. We then derive the competing dynamics before and after overload. Without overload, a strictly stronger influence asymptotically approaches dominance. Under overload, users become progressively less sensitive to influence strength, limiting further amplification and driving relative shares toward stable values determined by the initial state, strengths, and overload timing. We derive a first-order approximation to the exponential post-overload dynamics and evaluate its accuracy numerically. Experiments use six real network topologies but simulated competitive diffusion; they test internal predictions and structural sensitivity, not whether real users undergo the posited behavioral transition. Results are robust to alternative overload functions but sensitive to label-dependent priority cues. Recovering missing links can improve overload-time and final-share estimates, although link-prediction accuracy does not necessarily imply better diffusion prediction. Overall, information overload can interrupt cumulative strength amplification and thereby sustain coexistence under the stated assumptions.