Decay effect in the Lanchester model: The case of a growing market

The paper takes into consideration a growing market in which two companies compete by defensive, offensive and generic advertising activities. In contrast to earlier work in advertising competition, the Lanchester model is modified to include two significant factors from the economic point of view. First, the assumption about a growing market allows us to analyse the competition via offensive advertising for a potential market. Second, it is assumed, in contrast to previous studies, that the market share without advertising efforts declines. Thus, the decay rate is incorporated into the new model. The paper studies a differential game played over a finite horizon and provides closed-form expressions for equilibrium advertising strategies and market share trajectories in many cases. Additionally, the sensitivity of these equilibria is analysed. The results show how the combination of competition and market growth has a relevant influence on the policies of the companies under the assumption that the market share declines without advertising