Priority coalitional games and claims problems

In this paper, we analyze priority coalitional games as an extension of balanced games with transferable utility. Here, conditions imposed by a stable allocation used in the past need to be respected when deciding on a new allocation of the revenues obtained by the grand coalition. Using claims problems as a tool, we define weak and strong priority games with respect to a given allocation and a priority coalition, and study their properties and core. In the weak priority game, the value of a coalition reflects that coalitional members with priority should not be harmed, i.e., the coalitional value should never be below their total benefits according to the initial allocation. In the strong priority game, in addition to the previous condition, players outside the coalition that are not in the priority group should not harbour aspirations exceeding those benefits given by the initial allocation. Priority games are also extended to analyze cooperation restricted by a hierarchical structure. These games restrict the core so that desirable monotonicity properties are satisfied when there is a hierarchy. This allows for reconciling core selection and monotonicity over a hierarchy.