Abstract: In practice, more and more durable goods manufacturers take use of warranty service to obtian the competitive advantage. Manufacturers provide warranty service for consumers who buy durable goods. Price, warranty period and warranty service expense are the main factors influencing manufactuer's profits, due to product warranty services affecting the consumer's utility. Duopoly firms provide the same durable goods with different quality in the market.Product failure is random and subject to exponential function. Duopoly firms provide free reparation service within warranty period. In this paper' price is defined as the decision variable, and the differential game model is constructed to discuss the effect of unit product warranty service expenses and quality period on the equilibrium price for duopoly firms. And then how the inferior manufacturer achieves the same price with the high quality manufacturer through warranty period strategy is analyzed and warranty service strategy is analyzed. Results indicate that the higher the unit product warranty service expenses of duopoly firms and the longer the warranty period,the equilibrium price is higher.But the relationship between the consumer utility influence coefficient and unit product warranty service expenses affects the change of competitor's equilibrium price.The inferior manufacturer providing low quality products makes use of the strategies of increasing unit product warranty service expenses and extending warranty period to realize the same price with the high quality manufacturers under the equilibrium. In addition,the effects of different strategies of the inferior manufacturer on warranty cost are compared, and it is found out that the strategy of increasing unit product warranty service expenses is better than extending warranty period strategy. Finally, numerical analysis are used to further verify the effectiveness of the conclusion. So this paper not only provides theoretical guidance for manufacturers to implement warranty service, but also extends the scope of warranty service research.

Key words: differential games, durable goods, warranty period, warranty service expenses, equilibrium price