Underground natural gas storage facilities are vital to the operation of energy networks. Given the inelastic nature of the supply capacity and the high volatility of demand, storage acts as a buffer that facilitates physical delivery at peak demand periods and also smooths the price of gas. Operational efficiency is important for the overall cost-effectiveness of gas and electricity networks and is therefore deserving of study. We study the effects of competition when firms share space, the injection/withdrawal of resources and game-theoretic behavior. We present a game-theoretic model in which strategic interaction occurs between firms due to the interdependencies that arise given the uniform pressure level in the store. In our model, firms are traders that seek to lock in the intrinsic value of storage at the outset of the term by buying and selling forward contracts subject to physical flow constraints. We conduct an empirical analysis using fictitious play and a setup representative of actual facilities and observable forward curve prices. Our results indicate that large losses can occur during the withdrawal season when the forward curve has a specific shape. This motivates the need for alternative economic mechanisms to counteract strategic manipulation.