Abstract: This paper studies competitive brand advertising and cooperative generic advertising strategies in the market with a dominant firm and a weak firm,and gives a Stackelberg game model. Then,the equilibrium brand advertising,generic advertising,value function and the equation of market sharing are obtained from the model with Hamilton-Jacobi-Bellman equation. The research shows that the sale and the profit of the dominant firm and the weak firm in cooperative strategy are higher than that in non-cooperative strategy respectively. Furthermore,the generic advertising costs of the dominant,the weak and the industry are higher than that in non-cooperative strategy respectively.

Key words: market share, brand advertising, cooperative generic advertising, differential game, feedback Nash equilibrium, Hamilton-Jacobi-Bellman equation