Finitely Loyal Customers, Switchers, and Equilibrium Price Promotion

This present paper aims to provide some new perspectives on how firms' price promotional decisions may depend on different levels of brand loyalty and switcher population. We present a duopoly model with a segment of price‐sensitive switchers and a segment of customers who are loyal to one of the two brands but have limited brand loyalty. Our unique equilibrium splits into three types, depending upon configurations of brand strength and switcher population. The type of equilibrium for high brand loyalty corresponds to the one in Narasimhan. The remaining two types for intermediate and low brand loyalty demonstrate strikingly different properties. First, the strong brand has a higher price range and a higher regular price. Second, the strong brand has a higher (lower) average promotional depth than the weak brand when the switcher population is small (large). Third, both brands promote equally frequently when brand loyalty is relatively low.