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This article is about the fallacy the U.S. Supreme Court has made in it’s decision on Amex Express case. The decision was based on the theory that credit-card payment services market is a typical two-sided market. However, the credit-card payment service market is different from general two-sided market in many ways; It is not a typical transaction two-sided plaform Filistulicchi named. The decision put emphasis on the fact that the credit-card network has characteristics of two-sided market, which is indirect network effects. But a two-sided market can be analysed by the modern economic theory without any modification. Second, credit-card payment services market should be defined as a single market which single kind of service is provided. The Court held that two kinds of services are provided in the credit-card payment services market, but, the two services should be understood as one because the services are provided by one provider and are simultaneously consumed jointly two consumers. Dissidents criticized those reasoning because the services for cardholders and the sercices for merchants can not be consiered substitutes in consumption. Third, The Court did not anlyze why credit-card networks may force merchants to accept the agreement in which anti-steering clause is included. Fourth, anti-steering clause obstructs cardholders from aquiring information on cheeper alternatives, which has weekened price competition among credit-card networks. It is therefore not necessary for plaintiffs to prove that Amex’s anti-steering clause increased networks’ services costs above competition level nor that the output was restricted. But the Court required plaintiffs to prove it. Fifth, the Court did not infer competition injury from the anti-steering clause because the output of credit-card transactions grew dramatically from 2008 to 2013. But this evidence does not guarantee it has no anticompetitive effects. Sixth, It is a contradiction to reason that Amex’s high merchant fee increased competition among credit-card networks while also arguing that competitors decreased merchant fee to compete with other networks. In conlusion, the Court paid too much attention to the Amex’s jutification in profit maximizing strategy and too little attention to the anti-steering clause which results in anti-competitive effects.