This paper deals with a duopolistic industry, where the current sales of each firm is proportional to its goodwill stock. The authors analyze a duopoly, where each player’s advertising effort has the dual role of influencing positively his own goodwill and negatively the competitor’s one, and consider the circumstances under which a firm finds it optimal to remain in or exit the industry. Describing this model as a differential game with controls of advertising strategies, they investigate optimal controls for players and Nash equilibrium. Some examples are presented.