We analyze platforms in two-sided markets with network externalities, using the specific context of a payment card association. We study the cooperative determination of the interchange fee by member banks. The interchange fee is the ``access charge'' paid by the merchants' banks (the acquirers) to cardholders' banks (the issuers). We develop a framework in which banks and merchants may have market power and consumers and merchants decide rationally on whether to buy or accept a payment card. After drawing the welfare implications of a cooperative determination of the interchange fee, we describe in detail the factors affecting merchant resistance, compare cooperative and for-profit business models, and make a first cut in the analysis of system competition.
Rochet et al. (Tue,) studied this question.