Meca, et al. (2004) studied a class of inventory games which arise when a group of retailers who observe demand for a common good decide to cooperate and make joint orders. In this paper, the authors extend their model to the situation where the manufacturer provides the retailers with a price discount on purchases in excess of a certain order quantity. The authors define the corresponding inventory game with quantity discount, and show that the inventory game has a nonempty core. Then, the authors propose a core allocation rule, the demand-proportionality rule, and characterize it by introducing efficiency, the retailer splitting property and continuity.