IJPAM: Volume 60, No. 2 (2010)

MARKETING COMPETITION IN
THE MIDDLE OF PRODUCT LIFE-CYCLE:
A DIFFERENTIAL GAME ANALYSIS

N.G. Medhin$^1$, Wei Wan$^2$
$^1$Department of Mathematics
North Carolina State University
Raleigh, NC 27695, USA
e-mail: [email protected]
$^2$Department of Mathematics
Claflin University
Orangeburg, SC 29115, USA
e-mail: [email protected]


Abstract.The growth of market sale of a new product is followed by approximately stable market sales for some interval of time. The duration of this period depends on the kind of product. Because of the approximately constant sale volume, the basic dynamic of this stage is different from the first stage of product life cycle. In this paper a differential game model is used to get insight into the competition for one-product-market-share in the middle of the product life cycle in ${\mathbf n}$-company competition environment. In the model, Lanchester competition dynamic will be adopted. And two kinds of competition strategies and their interactions will be considered. Both open-loop and closed-loop controls will be considered. Two algorithms are designed for the computation of the equilibrium, and numerical results are reported and discussed. Valuable results about the difference between open-loop and closed-loop control are obtained from the numerical results, which are beneficial for practical decisions.

Received: January 27, 2010

AMS Subject Classification: 49K99, 49L99, 49M05, 49J21

Key Words and Phrases: differential games, numerical methods, marketing competition

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 2