This article studies the impact of modular assembly on supply chain efficiency. In the modular assembly approach, a manufacturer acquires pre-assembled modules from its suppliers, rather than the individual components, as in the traditional assembly approach. We analyze the competitive behavior of a two-stage modular assembly system consisting of a manufacturer, and a supplier who pre-assembles two components into a module. The firms can choose their own inventory policies and we show the existence of Nash equilibrium in the inventory game. Moving from the traditional to the modular approach has a twofold effect on the supply chain. First, we investigate the effect of centralizing the component suppliers. It can be shown that when there is no production time shift, the module supplier always holds more component inventories than suppliers do in the traditional approach, which yields a lower cost for the manufacturer. However, the suppliers, and therefore the supply chain may incur a higher cost in the modular approach. Second, we study the effect of a shift in production time from the manufacturing stage to the supplier stage. From numerical studies, it has been found that such a lead time shift always benefits a centralized supply chain, but not necessarily so for a decentralized system. Combining the two effects, we find that the modular approach generally reduces the cost to the manufacturer and the supply chain, which explains the prevalence of modular assembly from the perspective of inventory management. These results also provide some insight into how firms can improve supply chain efficiency by choosing the right decision structure and lead time configuration.