Hangfei GUO

Date of Award


Degree Type


Degree Name

Master of Philosophy (MPHIL)


Computing and Decision Sciences

First Advisor

Dr. LENG Mingming


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 prices for multiple products in a credit card network. In the first setting, we investigate a two-stage game problem in which the issuer and the acquirer first negotiate the interchange fee rate, and the acquirer and the retailer then determine their merchant discount rate and retail prices, 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 decisions. We derive both the Shapley value- and the nucleolus-characterized unique rates for the grand coalition. Comparing the two game settings, we show 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 sufficiently low operation costs. We also find that the large, highly-specialized merchants and banks are more likely to join the cooperative negotiation whereas the small firms may prefer the two-stage game setting. Our numerical experiments demonstrate that the acquirer's and the issuer's unit operation costs more significantly impact both rates in the cooperative game setting than in the two-stage game setting.


interchange fee rate, merchant discount rate, Nash bargaining, Stackelberg game, supermodularity, Shapley value

Recommended Citation

Guo, H. (2011). Interchange fee rate, merchant discount rate, and retail prices in a credit card network: A game-theoretic analysis (Master's thesis, Lingnan University, Hong Kong). Retrieved from

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