INTRODUCTION: This paper presents a distributed approach to optimise self-consumption on a local energy community containing photovoltaic generators, electric vehicles, loads and a storage system. OBJECTIVES: The goal is to maximise energy sharing between users while preserving the indivual objectives of each user. METHODS: Game theory is employed to model users' behavior and preferences. A distributed algorithm is used to solve the optimisation problem. In addition, a physical model of the grid is built to verify if the solutions respect grid constraints. Finally, a private blockchain environnement is deployed to concretely implement this distributed framework with a smart contract. RESULTS: It is shown that the proposed approach effectively leads to an increase of self-consumption rate on the local grid. CONCLUSION: The proposed distributed framework, combining game theory and blockchain, shows real potential to improve energy sharing on energy communities.