Loyalty Inducing Programs and Competition with Homogeneous Goods

Abstract

We analyze a market where two firms producing a homogenous good compete by means of two mechanisms: prices and a loyalty reward. We assume that firms act simultaneously when posting their loyalty reward and prices. Consumers who purchase from a firm in the first period lose the reward if they switch providers in the second period. They fully anticipate the effects on future prices of accepting the future bonus and maximize their total surplus over both periods. We first show that there is no equilibrium with prices and rewards equal to zero. We then show the existence of a SPNE where firms are able to obtain half the monopoly profits using large rewards as well as high prices in the second period. We completely characterizeall the symmetric equilibria of the game and show that, ingeneral, firmsobtain positive profits even when they compete in prices, the good is homogenous, and consumers are forward-looking. Finally we show that if firms are allowed to discriminate between old and new customers, the standard zero price Bertrand equilibria reappear.