Allocating pooled inventory according to contributions and entitlements

Abstract

Inventory pooling, whether by centralization of stock or by mutual assistance, is known to be beneficial when demands are uncertain. But when the retailers are independent, the question is how to divide the benefits of pooling. We consider a decentralized inventorypooling scheme where a retailer’s entitlements to the allocation during a shortage depend on his/her contributions to the pool. We derive the Nash equilibrium and specialize it to symmetric cases.