Localized and non-localized competition in the presence of consumer lock-in

In this chapter we model localized competition between firms when consumers exhibit brand lock-in or loyalty. We derive the symmetric equilibrium mixed strategy price distribution under two alternative models, and compare them to symmetric equilibrium strategies under non-localized competition. Contrary to the conventional wisdom in the product differentiation literature, the expected posted prices of firms are lower with localized competition. The analysis questions the robustness of models of product differentiation which ignore consumer lock-in.