n-Person cooperative games with transferable utility: I. The formation of coalitions

The paper considers the way that players and subcoalitions bargain with each other to form the grand coalition before play occurs. A digraph can be used to describe a particular coalition structure and it is argued that there exists an imputation for each structure. It is shown that there exists at least one subcoalition which loses if a coalition breaks up. So the ‘optimal’ structure consists of indissoluble coalitions, and the resulting digraphs are trees. Arguments are presented for a preference rule which says that for three subcoalitions, two will prefer to join together and then join with the third rather than all three joining together simultaneously. The optimal tree is thus a binary tree.