A new mixed integer programming formulation is proposed for hub-and-spoke network design in a competitive environment. It addresses competition between a newcomer liner service provider and an alliance, both operating on hub-and-spoke networks. The newcomer company maximizes its market share — proportional to service time and transportation cost —by locating a predefined number of hubs at candidate ports and designing its network. While general-purpose solvers do not solve instances of even small size, an accelerated lagrangian method coupled with a primal heuristic obtains very good bounds. Our computational experiments on real instances of practical size indicate superiority of our approach.