Core and nucleolus of covering games

A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between the players can be done using the co re concept, that is the set of all undominated cost allocations which preve nt players from grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integer covering problem. We g ive necessary and sufficient conditions for the core to be nonempty and cha racterize its allocations using linear programming duality. We also discuss a special allocation, called the nucleolus. We characterize that allocatio n and show that it can be computed in polynomial time using a column genera tion method.