This paper deals with a pie allocation problem to users, who are divided intosharing groups, that are not necessarily disjoint. The pie is allocated among the groups, rather than the users. The portion of a sharing group is a public good for its members, that is, all of them can enjoy it. A non-cooperative game for allocating the pie and a special equilibrium outcome,strongly disappointment-free allocation, are defined. We prove the existence of a unique such allocation and show that it coincides with the Nash solution of the related bargaining problem.Journal of Economic LiteratureClassification Numbers: C70, C71, C72 and C78.