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This article analyses the capabilities of digital platforms from an economics of convention perspective. This approach allows us, on one hand, to consider two-sided markets as exchange conventions arranged by platforms through a triangulation process, and on the other hand, to define their capabilities as being cognitive and based on socio-technical devices. Based on two case studies from the passenger transport sector, Uber and Blablacar, we show that the search for a level of equilibrium and a test of this level constitute, jointly, the conditions for the exploitation of two-sided markets, and that the organizational control of these conditions forges the capabilities of digital platforms. We built a taxonomy of capabilities and detail the two organizations capabilities.<br/>JEL Codes: L22, D25, L86, L91