A Dynamic Advertising Game with Market Growth

Abstract

The paper considers a market in which two firms compete on advertising over time. Each firm can use three types of advertising: offensive advertising which attempts to attract customers from the rival firm, defensive advertising which aims at protecting a firm’s customer base from the rival’s attacks, and generic advertising to make industry sales grow. We address questions like: How should a strategy for the simultaneous use of the three types of advertising be designed? How would the resulting time paths of sales look like? The paper studies a differential game played over an infinite time horizon and provides closed-form expressions for equilibrium advertising strategies and sales rate trajectories.