Interchange fee rate, merchant discount rate, and retail prices in a credit card network: A game-theoretic analysis

Abstract

We consider two game-theoretic settings to determine the optimal values of an issuer's interchange fee rate, an acquirer's merchant discount rate, and a merchant's retail price in a credit card network. In the …rst setting, we investigate a two-stage game problem in which the issuer and the acquirer …rst 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 "H.R. 2695," 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 …nd 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 "H.R. 2695"is 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.