The Shapley value is in the core of the energy game

Let $G=(V,E)$ be a graph, with the energy game assigning each coalition its graph energy and with $\boldsymbol{\varphi}$ denoting the Shapley value. Energy-game core conjecture. For the energy game, the Shapley value is in the core. This conjecture asks whether the Shapley allocation satisfies all coalition inequalities for graph energy; the source gives an example showing that the energy value itself need not coincide with the Shapley value, but provides no resolution of the core-membership question.