Current electricity tariffs do not reflect the real costs that a customer incurs to a supplier, as units are charged at the same rate, regardless of the consumption pattern. In this paper, we propose a prediction-of-use tariff that better reflects these costs, which asks customers to predict a baseline consumption, and charges them based both on their actual consumption, and the deviation from their prediction. We show how under this tariff no customer would have an incentive to consume in excess of their actual needs, and derive closed form expressions for their optimal prediction and expected payments. Second, using principles from cooperative game theory, we study how customers can collectively reduce their potential deviation by aggregating under a group-buying scheme. We prove that the associated cost game is concave, which means grouping reduces the total expected bill and that this payment can be fairly allocated among customers by their Shapley values. Third, considering a model where customers can join the group online, we propose marginal payment allocation schemes that incentivise them to commit early, thus preventing start-up inertia. Finally, we validate our model using real data from a set of 3000 consumers from the UK.