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In this paper, we develop the models for ports to select the best price and service time guarantee to maximize their operating profit under port competition and cooperation. We first analyze the optimization problem for the individual ports and then study the equilibrium solution in a multiple-port competition and the optimal solution in a multiple-port cooperation. Using a numerical study, we further examine the competitive advantage of a dominant port and perform comparison analysis between port competition and cooperation. Our results suggest that, whether the ports compete or cooperate, the dominant port has the largest profit and demand and does not necessarily offer the best service time guarantee. Furthermore, the price of each port chosen under competition is always lower than that chosen under port cooperation, whereas the service time guarantee of each port chosen under competition is always shorter than that chose under port cooperation. The demand difference and profit difference among all ports under port cooperation are smaller than those under port competition. Both the total demand and total profit under port cooperation are greater than those under port competition.