Two solution concepts for TU games with cycle-free directed cooperation structures

For arbitrary cycle-free directed graph games tree-type values are introduced axiomatically and their explicit formula representation is provided. These values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. The main property for the tree value is that every player in the game receives the worth of this player together with his successors minus what these successors receive. It implies that every coalition of players consisting of one of the players with all his successors receives precisely its worth. Additionally their efficiency and stability are studied. Simple recursive algorithms to calculate the values are also provided. The application to the water distribution problem of a river with multiple sources, a delta and possibly islands is considered

Two solution concepts for TU games with cycle-free directed cooperation structures

For arbitrary cycle-free directed graph games tree-type values are introduced axiomatically and their explicit formula representation is provided. These values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. The main property for the tree value is that every player in the game receives the worth of this player together with his successors minus what these successors receive. It implies that every coalition of players consisting of one of the players with all his successors receives precisely its worth. Additionally their efficiency and stability are studied. Simple recursive algorithms to calculate the values are also provided. The application to the water distribution problem of a river with multiple sources, a delta and possibly islands is considered

Networks, Communication and Hierarchy: Applications to Cooperative Games

Agents participating in different kind of organizations, usually take different positions in some network structure. Two well-known network structures are hierarchies and communication networks. We give an overview of the most common models of communication and hierarchy restrictions in cooperative games, compare different network structures with each other and discuss network structures that combine communication as well as hierarchical features. Throughout the survey, we illustrate these network structures by applying them to cooperative games with restricted cooperation