Modeling Advertising Expenditures Using Differential Equations: The Case of an Oligopoly Data Set

Abstract

The purpose of this paper is to examine the possibility of applying differential equations in the case of the advertising expenditures of firms, operating in an oligopoly. In this research, a generalization of the Lanchester’s combat model, will be used to examine the aforementioned case. Lanchester’s combat model assumes that only two military forces are fighting each other. The advertising expenditures data which will be examined come from the mobile communications market in Greece. This market can be characterized as an oligopoly, as the three examined firms own the 97.8% of the share. After setting the needed theoretical assumptions, Lanchester’s combat model can be applied. The research results indicate a good fit of the models’ predictions to the observed values which means that combat models are applicable in the field of business under the right conditions.