This paper presents a model of competing payment schemes. Unlike previous work on generic two-sided markets, the model allows for the fact that in a payment system, users on one side of the market (merchants) compete to attract users on the other side (consumers, who may use cards for purchases). It analyzes how competition between card associations and between merchants affects the choice of interchange fees, and thus the structure of fees charged to cardholders and merchants. Implications for other two-sided markets are discussed.