This report investigates how competition agencies can respond to the challenges posed by the multi-sided nature of platform markets, which are particularly common in the digital economy. It asks whether the antitrust tools that are traditionally used to define markets, to assess market power and efficiencies, and to assess the effects of exclusionary conduct and vertical restraints, remain sufficient to address those questions in the context of multi-sided platform markets. It then proposes how these tools might be re-designed or re-interpreted in order to equip competition agencies with the tools they require when analysing these markets.