Interchange Fee Rate, Merchant Discount Rate and Retail Pricing Decisions for a Credit Card Network: A Game-theoretic Approach

We consider two game-theoretic settings to determine the optimal values of an issuerís interchange fee
rate, an acquirerís merchant discount rate, and a merchantís retail price in a credit card network. In
the Örst setting, we investigate a two-stage game problem in which the issuer and the acquirer Örst
negotiate the interchange fee rate, and the acquirer and the retailer then determine their merchant
discount rate and retail price, respectively. In the second setting, motivated by the recent U.S. bill
ìH.R. 2695,î we develop a three-player cooperative game in which the issuer, the acquirer, and the
merchant form a grand coalition and bargain over the interchange fee rate and the merchant discount
rate. Following the cooperative game, the retailer makes its retail pricing decision. We derive both
the Shapley value- and the nucleolus-characterized, and globally-optimal unique rates for the grand
coalition. Comparing the two game settings, we Önd that the participation of the merchant in the
negotiation process can result in the reduction of both rates. Moreover, the stability of the grand
coalition in the cooperative game setting may require that the merchant should delegate the credit
card business only to the issuer and the acquirer with su¢ ciently low operation costs. We also show
that the grand coalition is more likely to be stable and the U.S. bill ìH.R. 2695îis thus more e§ective,
if the degree of division of labour in the credit card network is higher as the merchant, the acquirer, and
the issuer are more specialized in the retailing, the acquiring, and the issuing operations, respectively