In cooperative games with transferable utility, the coalition surplus drives the allocation of worth among players to determine a value for the game.
A meaningful research question concerns the role of the surplus in the allocation to coalitions, as in generalised values.
In this talk, we start by defining a game graph, where nodes are coalitions and edges represent the marginal contribution of a coalition by joining with each of its disjoint coalitions.
An associated Poisson equation elicits a new generalised value named the Hodge Generalized Value(HGV).
We will provide a simple analytical formula for the role of the surplus of complementary coalitions in the game and axiomatically characterise di HGV akin to the Shapley Value by leveraging the axioms of the null coalition, average efficiency, bilaterality, constant sum, and linearity of generalised values.
Finally, we propose some generalisations of our construction on hypergraphs of coalitions.
 
Joint work with Antonio Mastropietro.