This electronic companion is part of the manuscript entitled “Blockchain-enabled local markets for sharing storage in energy communities” which has been exclusively submitted to the IEEE Innovative Smart Grid Technologies (ISGT) -- Middle East 2023 conference. It comprises the complete mathematical formulation for all market participants, the collection of Karush-Kuhn-Tucker (KKT) conditions for all models and the proofs for the equivalence of Equilibrium Model and Optimization Model. We show this way that market is efficient; the system is dispatched at the minimum social cost and no one is motivated to deviate from the market clearing outcomes. We also prove market’s revenue adequacy, which implies that the market operator never incurs a budget deficit. Finally, we provide some technical parameters and data used in the case studies.