Competition and cooperation of inventory policies between two retailers in a two-stage supply chain

We extend the serial 2-stage supply chain to the case of one supplier and two retailers. It is assumed that the external provider for the supplier has ample goods. If the supplier has an inadequate on-hand inventory, the allocation will be fixed in a certain proportion. We show the optimal inventory policies of the chain members in three cases: independent market noncooperative type, independent market cooperative type, and absolutely competitive type.