Competitive influence maximization in voter dynamics: The role of timing and network heterogeneity

Abstract

In the study of influence maximization, most existing research often assumes a one-off resource allocation at the start of a competition. As a result, they overlook the benefits of dynamic, time-sensitive strategies. To overcome this limitation, we propose a novel approach using inter-temporal allocations within a non-progressive voter model to optimize the timing and distribution of limited resources for maximizing opinion spread. Our objective is twofold: (i) to provide understanding of patterns of opinion spread in complex networks subject to inter-temporal control, and (ii) to use insights from (i) to develop optimization strategies that balance resource constraints and temporal dynamics. Specifically, our study examines two scenarios: a constant-opponent setting and a game-theoretical framework. In the constant-opponent setting, we find that network heterogeneity significantly influences optimal campaign timing, with late initiation benefiting short time horizons in heterogeneous networks and early starts favoring longer horizons. To further enhance this strategy, we introduce a node-specific optimization strategy that outperforms uniform approaches, especially under resource constraints. In the game-theoretical framework, our results reveal that resource-rich controllers tend to start campaigns early, while resource-limited controllers strategically delay to counter their opponent’s advantage. Through analytical approximations and simulations, we provide insights into the temporal dynamics of influence spread. These findings offer practical guidelines for designing effective influence campaigns in competitive and time-sensitive contexts, with applications in marketing, politics, and public health.