The Partition Lattice Value for Global Cooperative Games

We introduce a new value for global cooperative games that we call the Partition lattice value. A global cooperative game describes the overall utility that a set of agents generates depending on how they are organized in coalitions without specifying what part of that utility is each coalition responsible for. Gilboa and Lehrer (1991) proposed a generalization of the Shapley value to this family of games that may imply a big loss of information. Here we take an alternative approach motivated by how the Shapley value distributes payoffs in unanimity games. More precisely, we consider that each link in the lattice of partitions represents a contribution and use them to define our value. The Partition lattice value is characterized by five properties. Three of them are also used in the characterization of the Gilboa-Lehrer value and another is weaker that the fourth and last property of their characterization. The last property of our result is new and describes how are payoffs distributed among the coalitions in global unanimity games.