Games With Limited Communication Structure

In this paper we consider cooperative transferable utility games with limited communication structure, called graph games. Agents are able to cooperate with each other only if they can communicate directly or indirectly with each other. For the class of acyclic graph games recently the average tree solution has been proposed. It was proven that the average tree solution is a core element if the game exhibits superadditivity. It will be shown that the condition of super-additivity can be relaxed to a weaker condition, which admits for a natural interpretation. Moreover, the concept of subcore is introduced. Under the same condition it is proven that the subcore is a subset of the core and always contains the average tree solution and therefore is a non-empty refinement of the core.