Coordination in vendor-buyer inventory systems: on price discounts, Stackelberg game and joint optimisation

We consider a version of the Stackelberg game that is used to model discount pricing decisions in vendor-buyer supply chains. The game consists of a leader who is selling a product to one (or more) follower(s) who in turn sell it to the ultimate consumers. We define conditional strategy for the leader as a strategy where the transfer price offered by the leader is conditional upon the specific decision taken by the follower. We show that the leader's optimal conditional strategy can achieve perfect coordination. We then discuss the application of the result to specific models for discount pricing decisions in vendor-buyer inventory systems and interpret its implications for these models.