Optimal advertisement-innovation mix for maximizing the discounted flow of profit

Due to boom in telecommunications market, there is hectic competition among the cellular handset manufacturers. As cellular handset manufacturing industry operates in an oligopoly framework, often price-rigidity leads to non-price wars. The handset manufacturing firms indulge in product innovation and also advertise their products in order to achieve their objective of maximizing discounted flow of profit. It is of interest to see what would be the optimal advertisement-innovation mix that would maximize the discounted flow of profit for the firms. We used differential game theory to solve this problem. We adopted the open-loop solution methodology. We experimented for various scenarios over a 30 period horizon and derived interesting managerial insights.