This paper unveils the strong competition in container cargo between Hong Kong Port which has been emerging as an international maritime center since the 1970s and Shenzhen Port which has recently gained remarkable achievements in the Pearl River Delta region. Among various competing strategies, the study focuses on the long-term one in which two ports will decide to compete by investing in capacity. The purpose of this research is to examine their decision, making process and to suggest future strategic actions in the current situation. Within its scope, only economic profit brought back from the investment is considered. For this reason, an uncertain payoff two-person game model is developed where an uncertain factor of demand is involved. In applying Uncertainty theory (Liu, 2013), the two methods to solve the game are introduced, including uncertain statistics and the expected Nash Equilibrium strategy. The results obtained from this research generate meaningful suggestions for future competition plan for the two selected ports, which conclude that Shenzhen is the dominant port in this long-term strategy. Compared to existing works on the same topic, the paper shows its distinctiveness by studying the latest competitive situation with regard to the uncertain demand in the game model.