Pricing Interrelated Goods in Oligopoly
In this paper we propose a two-good model of price competition in an oligopoly where the two goods can be complements or substitutes and each retailer has a captive consumer base `a la Burdett and Judd (1983). We find that the symmetric Nash Equilibrium of this model features atomless pricing strategies for both goods. When the two goods are complements the prices charged by any retailer are, at least locally, negatively correlated so if one of the goods is priced high the other one is on a discount. This finding is supported by an empirical observation that simultaneous discounts of complements are infrequent. In contrast, if the goods are substitutes or independently valued the prices will be randomized independently unless the less valuable substitute is not sold at all. In the case of complements the retailers earn higher profit relative to the case of selling both goods only as a bundle. The ability to "discriminate" between the captives and the shoppers through keeping the sum of the two prices high while setting one of the prices low drives the result. Such discrimination is impossible when the goods are substitutes as consumers switch to buying the lower priced substitute. Additionally, we provide some insights on bundling in the price dispersion setting.
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