In this paper, a newly emerging duopoly market with a short life cycle is analyzed. The partially known information of market is characterized by the possibility distribution of the parameter in the demand function. Since the life cycle of the new product is short, how many products should be produced by two rival firms is a typical one-shot decision problem. Within the one-shot decision framework, the possibilistic Cournot equilibrium is obtained for the optimal production level of each firm in a duopoly market with asymmetrical possibilistic information. The analysis results show that the proposed approaches are reasonable for one-shot decision problems, which are extensively encountered in business and economics..