Review of Industrial Organization 13: 509–522, 1998.
© 1998 Kluwer Academic Publishers. Printed in the Netherlands.
A Dynamic Model of Advertising and Product
CLAUDIO A. G. PIGA
Department of Economics, University of York, Heslington, York, YO1 5DD, U.K.
Abstract. This paper analyses a differential game of duopolistic rivalry through time where ﬁrms can
use advertising and price as competitive tools. Two cases are considered whereby: (1) advertising has
the main effect of increasing market size and ﬁrms differ in production efﬁciency; (2) advertising has
both predatory and cooperative effects in a symmetric market. The former shows that market shares
and advertising shares are positively correlated and that market size increases with the difference
in ﬁrms’ relative efﬁciency. The latter highlights the differences in the feedback and open-loop
strategies. It is shown that ﬁrms’ advertising are strategic complements and that proﬁts are higher
in the feedback equilibrium because ﬁrms advertise more. The applicability of the model in markets
where franchise contracts and dealership agreements operate is also discussed.
Key words: Differential games, advertising, product differentiation, oligopoly.
JEL classiﬁcation: C72, C73, L13, M37.
This paper investigates the nature of dynamic advertising and price strategies using
a differential game.
It develops a model of duopolistic competition with a dif-
ferentiated product where ﬁrms can use multiple competitive tools. The dynamic
nature of the model originates with the assumption that the number of consumers
in the market varies over time as a consequence of the total industry advertising
outlays. We consider two related cases which differ with respect to the way in
which advertising is assumed to inﬂuence consumers’ behaviour.
In the ﬁrst, advertising is perfectly cooperative (Friedman, 1983a; Martin, 1993).
The investment by one ﬁrm determines an increase in the market size which ben-
eﬁts all the ﬁrms in the industry in the same way. Thus advertising is a pure
public good and, therefore, under-investment in advertising occurs as a result of
I am particularly indebted to Gianni De Fraja, Paul Dobson, John Hey, Peter Simmons, Alan
Sutherland, the General Editor of the journal and a referee for the useful comments to a previous
version of the paper. The usual disclaimer applies.
See Kamien and Schwartz (1991) and Fudenberg and Tirole (1991) for an extensive treatment of
differential games and related solution concepts. See also Fershtman and Kamien (1987), Driskill and
McCafferty (1989; 1996) and Reynolds (1987) for examples of linear-quadratic games of dynamic
competition. Reinganum (1981) deals with another class of differential games which, like the linear-
quadratic ones, can be solved analytically.