In this work, we consider dynamic influence maximization games over social networks with multiple players (influencers). The goal of each influencer is to maximize their own reward subject to their limited total budget rate constraints. Thus, influencers need to carefully design their investment policies considering individuals' opinion dynamics and other influencers' investment strategies, leading to a dynamic game problem. We first consider the case of a single influencer who wants to maximize its utility subject to a total budget rate constraint. We study both offline and online versions of the problem where the opinion dynamics are either known or not known a priori. In the singe-influencer case, we propose an online no-regret algorithm, meaning that as the number of campaign opportunities grows, the average utilities obtained by the offline and online solutions converge. Then, we consider the game formulation with multiple influencers in offline and online settings. For the offline setting, we show that the dynamic game admits a unique Nash equilibrium policy and provide a method to compute it. For the online setting and with two influencers, we show that if each influencer applies the same no-regret online algorithm proposed for the single-influencer maximization problem, they will converge to the set of $ε$-Nash equilibrium policies where $ε=O(\frac{1}{\sqrt{K}})$ scales in average inversely with the number of campaign times $K$ considering the average utilities of the influencers. Moreover, we extend this result to any finite number of influencers under more strict requirements on the information structure. Finally, we provide numerical analysis to validate our results under various settings.

This work has been submitted to IEEE for possible publication