Stability and Endogenous Formation of Inventory Transshipment Networks

This paper studies a cooperative game of inventory transshipment among multiple firms. In this game, firms first make their inventory decisions independently and then decide collectively how to transship excess inventories to satisfy unmet demands. In modeling transshipment, we use networks of firms as the primitive, which offer a richer representation of relationships among firms by taking the coalitions used in all previous studies as special cases. For any given cooperative network, we construct a dual price allocation under which the network is stable for any residual demands and supplies in the sense that no firms find it more profitable to form subnetworks. Under the allocation based on the marginal contribution of each firm to its network (called the MJW value), we show that various network structures such as complete, hub-spoke, and chain networks are stable only under certain conditions on residual amounts. Moreover, these conditions differ across network structures, implying that a network structure plays an important role in establishing the stability of a decentralized transshipment system. Finally, we consider the case when firms establish networks endogenously, and show that pairwise Nash stable networks underperform the corresponding networks in centralized systems.