Defensive, Offensive, and Generic Advertising in a Lanchester Model with Market Growth

The paper considers a duopolistic market in which firms compete over time through their respective advertising efforts. In contrast to earlier work in advertising competition, the paper supposes that each firm may choose among three types of advertising: offensive advertising which has the purpose of attracting customers from the rival firm, defensive advertising which aims at protecting a firm’s customer base from the competitors’ attacks, and generic advertising which aims at enhancing industry sales. We address questions like: How should an advertising strategy, for each of the three types of advertising effort, be designed? How would the corresponding time paths of sales look like? The paper uses differential game theory to answer these questions and provides closed-form analytical expressions for equilibrium advertising strategies and sales rate paths. It is found that advertising strategies can be expressed in terms of the shadow prices of the firms’ sales rates and the model parameters. Two combinations of theses advertising are optimal: all three advertising together and both offensive and defensive advertising. As to the latter, an essential assumption is that offensive advertising is more cost-effective than defensive advertising.