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Consider a duopoly market in which consumers have heterogeneous information about the quality differential q of the two goods. When firms are ignorant about q, consumers rationally believe that a firm with a high market share is likely to produce a highquality good. As a result, firms try to signal-jam the inferences of consumers and compete for market shares beyond the level explained by short-run profit maximization. When firms know q, multiple equilibria may exist, but under a regularity condition, there is one equilibrium in which market shares signal quality, and then the market tends to be more competitive.

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We thank Aleix Calveras and Ricard Flores for their useful comments. Ramon Caminal acknowledges the support of the CREA Barcelona Economics Program and the Spanish MCyT (grant SEC2002-02506).Many economists and policy analysts seem to believe that loyaltyrewarding pricing schemes, like frequent yer programs, tend to reinforce rms market power and hence are detrimental to consumer welfare. The existing academic literature has supported this view to some extent. In contrast, we argue that these programs are business stealing devices that enhance competition, in the sense of generating lower average transaction prices and higher consumer surplus. This result is robust to alternative speci cations of the rms commitment power and demand structures, and is derived in a theoretical model whose main predictions are compatible with the sparse empirical evidence.JEL Classi cation numbers: D43, L13