Shelf-space allocation of national and private brands

We propose a game-theoretic model in which one national-brand manufacturer, acting as a leader, maximizes her own profit and one retailer, selling the national brand and her private label and acting as a follower, maximizes her category profit. We characterize the resulting Stackelberg equilibrium in terms of the amount of shelf space allocated to these brands as well as their prices. The results suggest that the allocation of the shelf space depends on the quality of the private label. In our framework, quality is measured by the baseline sales (or brand equity), the degree of brand substitution and the price positioning.