Access to the global container liner shipping network is of crucial importance for international trade and the sustainable development of countries. Changes to the structure of this network, such as increased reliance on hub-and-spoke configurations driven by the introduction of larger container vessels or reduction of buffer times to minimise operational costs stand to alter the ability of the network to withstand disruptions. Such impacts on transport network vulnerability are often paradoxical or not intended. Understanding the extent to which changes in the configurations of liner shipping networks impact transport network vulnerability is of vital importance for public and private decision-makers of the maritime industry responsible for ensuring accessibility to global liner shipping services. This study proposes a game theoretic approach to identify most vulnerable components in liner shipping networks exposed to disruptive events such as loss of functionality in ports due to natural disasters or potential terrorist attacks. We develop a two-player, non-cooperative, zero-sum game between a malevolent agent who tries to maximise disruption costs and a network router who tries to minimise routing costs. A numerical example is presented where, at mixed strategy Nash equilibrium, the most vulnerable nodes and links are identified and the minimum cost routes for given origin destination pairs are found. Results are also used to identify sets of interventions that would increase the robustness of the network.