Least cores in energy community games
Giancarlo Bigi, Davide Fioriti, Antonio Frangioni, Mauro Passacantando, Davide Poli
TL;DR
The paper addresses stable reward allocation in energy communities by modeling them as Energy Sharing Games, a veto transferable-utility game with an indispensable aggregator. It develops the theory of the least core under both admission-fee regimes, providing exact formulas in the balanced no-fee case and computable bounds plus LP-duality methods when fees are present, along with detailed analysis of the aggregator's feasible shares. The results show that no-fee ESGs are always balanced with explicit least-core values, while fee-containing ESGs can be unbalanced with nonempty or empty cores, depending on the parameters, and yield practical bounds and computational techniques. The findings support designing fair and stable allocation schemes for real-world energy communities and offer guidance on when the aggregator should capture more of the total surplus; they also propose scalable computational approaches for determining least-core allocations.
Abstract
An energy community is modeled as a cooperative game, where a veto player is needed beyond the prosumers to manage the community, and the worth of a coalition is its benefit compared to the selfish behaviour of the prosumers. Properties of the game such as superadditivity, monotonicity, convexity and balancedness are analyzed both in the presence and absence of admission fees. Then, the least core and its value are studied in detail, underlying the differences between the cases where the game is balanced or not. In particular, exact formulas and computable bounds for the least core value are provided. Finally, the maximum and minimum reward in the least core for the veto player are analyzed.