Pricing and matching under duopoly with imperfect buyer mobility

Recent contributions have explored how lack of buyer mobility affects pricing. For example, Burdett, Shi, and Wright (2001) envisage a two-stage game where, once prices are set by the firms, the buyers play a static game by choosing independently which firm to visit. We incorporate imperfect mobility in a duopolistic pricing game where the buyers are involved in a multi-stage game. The firms are shown to have an incentive to elicit loyalty on the part of the buyers by giving service priority to regular customers. Then equilibrium prices are higher than under a static buyer game; further, they converge to their value under perfect buyer mobility as the number of stages of the buyer game increases.