Localized and Non-Localized Competition in the Presence of Consumer Lock-in

This paper models localized competition between firms when there is consumer 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, expected prices are lower with localized competition. The analysis questions the robustness of models of product differentiation which ignore consumer lock-in.