Abstract: As a status symbol, the private car can reflect the social status of the consumers in the consumption process. In the process of consumption of private cars, attention has been paid on the social status reflected of private cars in a certain extent. To a certain extent, this kind of conspicuous consumption explains that why China's car sales are increasing year by year despite traffic jams' inconvenience. From the perspective of the status utility of private cars and the impact of the cities' traffic conditions to the use of private cars, a differential game model of two firms offering quality differentiated private cars is built to analyze the impact of the status utility and the cities' traffic conditions to the marketing strategy of the firms of private cars. The results show that: both the firms' optimal dynamic prices and the optimal profits increase with the increase of the status utility, but decrease with the intensity of the cities' traffic congestion; and the impact is higher to the firm which its' private cars with a higher quality than to the firm which its' private cars with a lower quality; as the difference of quality level between the two firms increases, the difference of the impact increases; the change of each firm's optimal dynamic price with time is determined by the change relation of the status utility and the cities' traffic conditions. To make the right marketing strategy for the car manufacturers, as well as local government departments to formulate reasonable traffic control measures, the conclusions of this paper have certain significance.

Key words: the status utility, the cities' traffic conditions, quality differentiation, private car, differential game, prospect theory