In this paper, goodwill and quality management of two competing firms are analyzed in a differential game framework. A Lanchester model is used to represent market share competition where own attraction rate depends on own goodwill, while own abandon rate depends on own quality. The search for a Nash solution by a numerical algorithm leads to determine for each competitor the optimal advertising and quality improvement efforts under various initial configurations. Moreover, a study of key-factors of performance points out the most appropriate reengineering projects to be implemented by a small inefficient firm in order to better its competitive position.
EL OUARDIGHI, F. et PASIN, F. (2002). Quality Improvement and a Goodwill Accumulation in a Dynamic Duopoly. ESSEC Business School.