Least cores in energy community games

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, an exact formula and computable bounds for the least core value are provided, and the maximum and minimum reward in the least core for the veto player are analyzed. Finally, a few computational approaches for the exact formula are developed and tested.