We formulate a dynamic economic dispatch game in which each generator has its own electricity storage device. The operation of storage introduces time-coupling constraints. We focus on how the use of storage may affect the market structure and market outcomes in the locational marginal pricing mechanism. We first show that even when the independent system operation is unaware of the storage, there exists an efficient bid profile that induces the optimal dispatch. We then demonstrate that the use of storage does not increase the room for strategic play, but may improve the equilibrium outcomes. We provide sufficient conditions under which there exist efficient Nash equilibria. Furthermore, we propose the marginal contribution pricing mechanism that guarantees efficient outcomes.