Multi-player interactions and vertical relationships in the U.S. containerized-import shipment market are investigated using game theory approaches. Bi-level programming problems (BLPP) are built to capture the hierarchy structure of the container shipping industry, whereas the ocean carriers (OC) are considered as the market leader. For a case study with five players from several levels of the shipment chain, 16 BLPPs are built to analyze the 32 coalition possibilities. Two routes are compared: The West Coast route (WCR) includes one terminal (P1) and one railroad (R); the East Coast route (ECR) includes a second terminal (P2) and the Panama Canal (PC). The impact of Panama Canal expansion is investigated by comparing scenarios with different assumptions of vessel size. Capacity constraints at port terminals are also analyzed by assuming different capacity levels. The grand coalition of the five players is found to be very unstable because of the unavoidable competition within the coalition; hence, following games are further created, supposing the grand coalition could not form. Model results indicate the OC prefers to form an East Coast Coalition (ECC) with East Coast players if the grand coalition could not form. Sensitivity analyses on some parameter values for the grand coalition and for the ECC bring some interesting findings. With higher cargo values, the WCR becomes more appealing because of its quicker delivery time and lower inventory costs compared with the ECR. The Panama Canal expansion will improve market power and profit shares for the East Coast players if the canal operator could increase its competitive price more than the increase of costs. Generally, a player will gain more market power if its cost could be reduced. A player's upper bound rate is a reflection of its relative market power. But in a complicated market characterized with various cooperation-competition strategies and an ambiguous definition of partners and competitors, the impact of a player's upper bound rate on the market power structure could not be easily explained. For future research, the challenge mainly lies on the large number of BLPPs that need to be constructed and solved in order to study more players.