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Two-sided platforms serve two sets of customers and enable them to interact with each other. The five most valuable corporations in America – Amazon, Apple, Facebook, Google, and Microsoft – all operate two-sided platforms. But despite their growing power, the Supreme Court's American Express decision has made it harder to stop them from stifling competition. This Article systematically exposes the flaws in the Court's reasoning and identifies the principles that should govern future cases. The Court’s most fundamental error was to require plaintiffs in rule of reason cases to make an initial showing of consumer harm that weighs the effects of the defendant's conduct on both sides of its platform. This unprecedented approach will discourage antitrust litigation. It is also flawed antitrust policy because it allows a firm to exploit customers on one side of its platform to benefit customers on the other side. I argue that such conduct by a platform should only be permissible in the face of a market failure - an obstacle that prevents the market from maximizing consumer welfare. Without a market failure - and American Express (Amex) could not demonstrate one - competition will produce the optimal allocation of benefits across a platform. This article shows why the Court was wrong to treat Amex's two sets of customers - cardholders and merchants - as a single market. Instead, it offers a better approach to discerning market power in antitrust cases, based on the likely effects of the defendant's conduct. Under this approach - and contrary to the Court's conclusion - Amex possessed market power, as its steering ban almost certainly enabled it to maintain its merchant fees above the competitive level. The Article concludes that American Express was deeply flawed, and that courts should confine it to its facts and follow the principles set forth in this Article.