Paying for loyalty: product bundling in oligopoly

In recent times, pairs of retailers such as supermarket and retail gasoline chains have offered bundled discounts to customers who buy their respective product brands. These discounts are a fixed amount off the headline prices that allied brands continue to set independently. In this paper, we model this bundling using Hotelling competition between two brands of each product. We show that a pair of firms can profit from offering a bundled discount to the detriment of firms who do not bundle and consumers whose preferences are farther removed from the bundled brands. Indeed, when both pairs of firms negotiate bundling arrangements, there are no beneficiaries (the effect on equilibrium profits is zero) and consumers simply find themselves consuming a sub-optimal brand mix. If the two separate products are owned by the same firm, additional complications arise although if both product sets are integrated, no bundled discounts are offered in equilibrium.