This paper analyses market competition between two different types of credit card platforms: not-for-profit associations and proprietary systems. The main focus is on the role of the interchange fee set by not-for-profit platforms. We show that when the interchange fee is set so as to maximise the sum of issuers' and acquirers' profits, the equilibrium values of platforms' profits, of the sum of the fees charged by each platform and their market shares are independent of the competitive conditions within the not-for-profit platform and are affected by the strength of inter-platform competition. We also show that the imposition of a ban on the setting of the interchange fee has ambiguous effects on the profit of the proprietary system.
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