Interchange fee rate, merchant discount rate, and retail price 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 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 price, respectively. In the second setting, motivated by the recent US 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 find 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 show that the grand coalition is more likely to be stable and the U.S. bill “H.R. 2695” is thus more effective, if the degree of division of labor in the credit card network is higher as the merchant, acquirer, and issuer are more specialized in the retailing, acquiring, and issuing operations, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

A fair staff allocation rule for the capacity pooling of multiple call centers

“…According to online Appendix A, Shapley value (Shapley [21]) and the nucleolus (Schmeidler [20]) are the two commonly-used solutions each representing a unique, fair imputation (sta¤ allocation scheme for our sta¢ ng problem). However, to obtain the nucleolus solution, one needs to solve a series of linear programming (LP) problems (Wang [27]); for recent applications in the business area, see Guo, Leng, and Wang [10] and Leng and Parlar [15]. Due to the complexity of the nucleolus, we shall avoid this solution in this note.…”

Using cooperative game theory to contribute to strategy research

“…The authors consider the ramifications of different CGT solution concepts, and do not allow for transferrable utility because transfer pricing not only affects value capture but also the incentive of each division to create value. Guo, Leng, and Wang () offer two models of a credit card network, in each case considering a variety of CGT solutions. In one model, CGT is used to model bargaining between the issuer and acquirer over the interchange fee, and the acquirer then plays an NGT pricing game with a merchant over the discount rate; in the other model, CGT is applied to three‐way bargaining among these players over all pricing elements.…”