Inventory centralization games with price-dependent demand and quantity discount

Consider a distribution system consisting of a set of retailers facing a single-period price-dependent demand of a single product. By taking advantage of the risk-pooling effect and the quantity/volume discount provided by suppliers or third-party carriers, the retailers may place joint orders and keep inventory at central warehouses before demand realization, and allocate inventory among themselves after demand realization to reduce their operating costs. Under rather general assumptions, we prove that there is a stable allocation of profits among the retailers in the sense that the resulting inventory centralization game has a nonempty core. We also show how to compute an allocation in the core.