This article explores the potential of blockchain technology in enabling a new system of value that will better support the dynamics of social sharing. Our study begins with a discussion of the evolution of value perceptions in the history of economic thought. Starting with a view on value as a coordination mechanism that defines meaningful action within a certain context, we associate the price system with the establishment of capitalism and the industrial economy. We then discuss its relevance to the information economy, exhibited as the techno-economic context of the sharing economy, and identify new modalities of value creation that better reflect the social relations of sharing. Through the illustrative case of Backfeed, a new system of value is envisioned, comprising three layers: (a) production of value; (b) record of value; and (c) actualisation of value. In this framework, we discuss the solutions featured by Backfeed and describe a conceptual economic model of blockchain-based decentralised cooperation. We conclude with a tentative scenario for blockchain technology that can enable the creation of commons-oriented ecosystems in a sharing economy.