Do strategic conclusions depend on how price is defined in models of distribution channels?

Models of distribution channels have defined retailer and manufacturer pricing decision variables in different ways, such as absolute retail price or absolute retail margin and absolute manufacturer price or absolute manufacturer margin. This article examines whether this choice of definition affects the equilibrium outcomes from such models. It shows that the equilibrium outcomes do not change with these definitions if manufacturers are modeled as Stackelberg pricing leaders to their retailer. However, if manufacturers are modeled as Bertrand-Nash competitors to their retailer or as Stackelberg pricing followers to their retailer, the equilibrium outcomes change depending on how the retailer's pricing decision variables are defined. Moreover, if in these two cases manufacturers and retailer are allowed to define their own pricing decision variables, then (1) manufacturers are indifferent about choosing among absolute prices, absolute margins, and percentage margins, but (2) the retailer chooses percentage margins. These results have implications for both theoretical and empirical models of price competition in distribution channels.