Summary: With the growing collection of sales and marketing data and depth of detailed knowledge of consumer habits and trends, firms are gaining the capability to discern customers of other firms from the potential market of uncommitted consumers. Firms with this capability will be able to implement a strategy where the advertising effort towards customers of competing firms may differ from that towards uncommitted consumers. In this work, dynamic models for advertising in an oligopoly setting with fixed total market size and sales decay are presented. Two models are described in detail: a nontargeted model in which the advertising effort is the same for both categories of prospective customers, and a targeted model that gives firms the capability to allocate effort across the two categories differently. In the differential game setting, open-loop and closed-loop Nash equilibrium strategies are derived for both models. Several strategic questions that a firm may face when practicing targeted advertising on a fixed budget are discussed and addressed.