Inventory and pricing policies for a duopoly of complements

We design and analyze two duopoly models for two competing sellers. Each seller is assumed to be a profit maximizing EOQ-based decision maker facing linear demand functions. We also assume that a single product is sold by each seller, and the two products of the two sellers are complements. Under these assumptions, in the first duopoly model, we develop a Cournot-type duopoly model where competition is over the selling quantity. In the second duopoly model, we develop a Bertrand-type duopoly model where competition is over the selling price. For both models, we derive and analyze equilibrium inventory and pricing policies. Various interesting numerical examples are illustrated.