The Liquefied Natural Gas (LNG) trade is one of the most promising sectors in energy shipping. It is expected that competition will increasingly develop in the shipping segment of the LNG chain, which at least in its first phases will have the characteristics of an oligopolistic market. The LNG shipping market context is appropriate for the adoption of a (non-cooperative) game theoretic analysis framework to support decision-making. This paper focuses on oligopolistic competition in LNG shipping over the transportation capacity supplied to a trade route by competing shipping companies. It also examines the possibility of non-cooperative collusion among the competing parties, in order for them to share higher profits. The conclusions concern the optimal level of capacity supply by the competitors, under certain interaction settings, and the conditions under which they can sustain Pareto efficient equilibria.