Price Promotions in Asymmetric Duopolies with Heterogeneous Consumers

In this note I investigate the outcome of a static price competition between a strong firm ( a firm with an established loyal consumer base) and a weak firm ( a firm without loyal consumers). The consumers are divided into the strong firm's loyal segment and the switching segment, members of which have heterogeneous tastes for the firms' products. In the presence of loyal consumers, for a large set of the parameters of the demand function, the firms use mixed strategies over a finite number of prices. These strategies can be interpreted as occurrences of sales. The most common case is that of the strong firm's using two prices and the weak firm's using one price. However, when both firms use sales, the weak firm promotes more often than the strong firm.