Shelf space allocation game with private brands: a profit-sharing perspective

This work examines the role of a non-price variable, shelf-space in inter-brand competition. The retailer introduces a private brand to control the prices of the national brand, which acts as a monopoly in the absence of any competition from other brands. The private brands compete with national brands for demand, which is a function of the allocated shelf space and the brand price. We propose a game-theoretic model involving a national brand and a private brand who compete horizontally in the supermarkets for shelf space. A comparative study is undertaken through two different cases. In the first case, the retailer promotes the private brand manufactured by itself followed by the second case wherein retailer sells the private brand produced by another manufacturer. The retailer allocates shelf space to both the national as well as private brand simultaneously to capture the competition. The manufacturer of the national brand acts as the stackelberg given its power of setting wholesale prices. The equilibrium of the profit maximization game is expressed in terms of prices, shelf-spaces and profit margin of the players. This work is an attempt to gain insights on the conditions of allocation which are profitable for the manufacturer taking into account the consumer preferences between competing brands. The study also indicates that manufacturer’s profits reduces when they compete for space and make the retailer dominant, when the latter is only involved in shelf space allocation without any in-house production. We contribute as building blocks to understand how shelf-space limitation intensifies the manufacturer-retailer competition and also obtain managerial insight on disproportionate distribution of profits.