A shelf-space-dependent wholesale price when manufacturer and retailer brands compete

We propose a game-theoretic model involving the manufacturer of a national brand and a retailer selling her private label along with the national brand. The retailer can use either a differentiation strategy or an imitation strategy for offering her store brand. We consider two cases: the benchmark case, where both players have symmetric information and play a Nash game, and the incentive case, where the national brand's manufacturer, acting as a leader, offers an incentive to the retailer in order to benefit from a larger proportion of the shelf space, which ultimately increases her own profit. By comparing both situations, we attempt to derive the conditions under which it is profitable for the manufacturer to implement such an incentive strategy and investigate if the results are idiosyncratic to the PL concept. These conditions are fourfold, and include the private label's image, the price competition between the national brand and the private label, the transfer price level and the shelf-space allocated to the national brand in the benchmark case.