TU-Games: Revisiting Fundamental Concepts

This article addresses conceptual shortcomings in literature on coalitional TU-games. We revisit and partly redefine key notions such as coalition , coalition function , efficiency , and duality , emphasizing their dependence on the class of TU-games under scrutiny. We also introduce a refined notion of a dual game, which aligns better with its typical interpretation and coincides with the classical version on superadditive games. Finally, we characterize the cohesive hull of a game via the duality theorem in linear programming, drawing parallels to the construction of the core via the Bondareva-Shapley theorem.