  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.
