Price competition with repeat, loyal buyers

Extant theoretical models suggest that greater consumer loyalty increases a firm’s market power and leads to higher prices and fewer price promotions (Klemperer, Quarterly Journal of Economics 102(2):375–394, 1987a, Economic Journal 97(0):99–177, 1987b, Review of Economic Studies 62(4):515–539, 1995; Padilla, Journal of Economic Theory 67(2):520–530, 1995). However, in some markets large, national brands that are able to generate more consumer loyalty than their rivals offer lower prices and promote more frequently. In this paper, we develop a two-period game-theoretic, asymmetric duopoly model in which firms differ in their ability to retain repeat, loyal buyers. In this market, we demonstrate that it is optimal for a firm that generates more loyalty to offer a lower average price and promote more frequently than a weaker competitor. Numerical analysis of a more general infinite period version of this asymmetric model leads to three additional results. First, we show that there is an inverted-U relationship between a weak firm’s ability to attract repeat, loyal consumers and strong firm profits. Second, we show that the relative ability of firms to attract repeat buyers affects whether serial and contemporaneous price correlations are positive or negative. Finally, we highlight the effect of dynamics on firms’ expected prices and profits.