A note on equilibria for two-tier supply chains with a single manufacturer and multiple retailers

A well-studied problem in the supply chain management literature considers a two-tier supply chain for a homogeneous product with a single manufacturer, multiple retailers and a general inverse demand function. The problem has been analyzed in the literature without a formal mathematical treatment of the existence/uniqueness of equilibria. Furthermore, the existence/uniqueness results derived for related models are not extendable to our model. The objective of this paper is to derive sufficient conditions for the existence/uniqueness of Stackelberg-Nash-Cournot equilibria for the two-tier problem.