Two-Stage Allocation Procedures

Suppose some individuals are allowed to engage in different groups at the same time and they generate a certain welfare by cooperation. Finding appropriate ways for distributing this welfare is a non-trivial issue. The purpose of this work is to analyze two-stage allocation procedures where first each group receives a share of the welfare which is then, subsequently, distributed among the corresponding members. To study these procedures in a structured way, cooperative games and network games are combined in a general framework by using mathematical hypergraphs. Moreover, several convincing requirements on allocation procedures are discussed and formalized. Thereby it will be shown, for example, that the Position Value and iteratively applying the Myerson Value can be characterized by similar axiomatizations.