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

Online and Offline Dynamic Influence Maximization Games Over Social Networks