Loyalty inducing programs and competition with homogeneous goods

We analyze a market where two firms producing a homogenous good compete by means of two mechanisms: prices and a loyalty bonus. We assume that firms act simultaneously when posting their loyalty bonus and prices. Consumers who purchase from a firmin the first period must return the bonus in case they switch providers in the second period. They fully anticipate the effects on future prices of accepting the bonus and maximize their total surplus over both periods. We first show that there is no equilibrium with prices and bonuses equal to zero. We then show the existence of a SPNE where firms are able to obtain half the monopoly profits using large bonuses in the first period and high prices in the second period. We completely characterize all the symmetric equilibria of the game and show that, in general, firms obtain 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 equilibria reappear. JEL Classification: L13.