Quality improvement and goodwill accumulation in a dynamic duopoly

This paper analyzes optimal advertising and quality improvement decisions by duopolist firms competing in a dynamic setting. An extended version of the Lanchester model is formulated where conformance quality and goodwill are both involved in competition for market share. Each competitor's new customer attraction rate depends on its own goodwill, while the disloyalty rate for current customers is influenced by the proportion of defective items. The search for a non-cooperative solution by qualitative as well as numerical means leads to definition of the optimal path for advertising and improvement efforts for each competitor, examined under a wide range of configurations.