Why do Payment Card Networks Charge Proportional Fees?

Abstract

I extend Shy and Wang's (2011) model and study the problem of successive monopoly when complementarity is imperfect. In my model, consumers value the good no matter they pay in cash or by card. However, they are willing to pay a higher price if they can enjoy additional card service. Since merchants can sell at a lower price without providing card service, their outside option imposes a participation constraint on the card network's maximization. I show that double marginalization does not arise as long as the constraint is binding, and the constraint is binding if and only if the degree of complementarity is smaller than a critical value. If double marginalization does not arise, the effects of proportional fees found in the S-W model become ambiguous.