I. Introduction

II. A Brief History of a Long Litigation ... A. The District Court Rules for Plaintiffs Based on a One-Sided Market Definition ... B. The Second Circuit Reverses, Applying a Two-Sided Market Definition ... C. The Supreme Court Affirms, Embracing a Two-Sided Market Definition

III. Lessons from Amex ... A. Lesson One: A Full Rule of Reason Analysis—Not Some Form of Relaxed Review Advocated by the Government—Applies to Vertical Agreements Between a Platform and Customers on One Side of the Platform ... B. Lesson Two: For That Rule of Reason Analysis, a Plaintiff First Must Define a Relevant Market That Includes Both Sides of Two-Sided Transaction Platforms

C. Lesson Three: When the Relevant Market Is Two-Sided, a Plaintiff Must Demonstrate That the Challenged Conduct Harmed Competition in the Market as a Whole

IV. Misperceptions About Amex ... A. Fallacy One: Two-Sided Market Definition Does Not Apply to “Mature” Platforms ... B. Fallacy Two: A Platform’s Conduct Should Be Condemned If Platform Consumers on One Side Are “Subsidized” by Those Who Do Not Use the Platform … C. Fallacy Three: Amex Will Complicate and Confuse Antitrust Analysis in a Wide Range of Cases