<p>This paper investigates dynamic advertising competition in duopoly markets operating over partially observed consumer networks. Traditional models often adopt impulse-like interventions that induce abrupt opinion changes; in contrast, we develop a continuous control framework motivated by the modern role of influencer marketing. By leveraging a linear time-invariant (LTI) system, we model consumer opinions as evolving through local interactions, where each firm allocates an advertising budget to a predetermined set of influencers. Recognizing that advertising efforts typically evolve more slowly than consumer opinions, our approach incorporates a two-timescale framework, enabling firms to steer the steady-state opinion profile in the presence of time-varying, unknown disturbances such as economic fluctuations. To address the challenge of incomplete information-arising from limited surveys—we propose a feedback strategy based on decentralized observers, ensuring robust estimation of the network state. Our analysis derives equilibrium strategies for the competing firms by extending time-varying optimization techniques to zero-sum games. This work not only advances theoretical understanding of dynamic competition over consumer networks but also offers practical guidelines for firms seeking to optimize advertising strategies under uncertainty and partial observability.</p>