We consider a homogeneous goods market with three
firms that are asymmetrical in loyals and switchers, and our
results clarify the varied price promotion strategies in equilibrium.
For example, we show that a firm can adopt a “partitioned”
pricing strategy that combines frequent, shallow
discounts to compete with a higher-priced firm and infrequent,
deep discounts to compete with a lower-priced firm.
Our results also explain a situation in which a small firm is
better off pricing high with little discounting, despite possessing
few loyals. In general, our model not only encompasses
a three-firm extension of prior duopoly models but
also explains previously ambiguous situations, such as
when a retailer has both few loyals and few switchers.