On the Core of Directed Acyclic Graph Games

Arbeitspapier

There lies a network structure between fixed tree and minimum cost spanning tree networks that has not been previously analyzed from a cooperative game theoretic perspective, namely, directed acyclic graph (DAG) networks. In this paper we consider the cost allocation game defined on DAG-networks. We briefly discuss the relation of DAG-games with other network-based cost games. We demonstrate that in general a DAG-game is not concave, even its core might be empty, but we provide an efficiently verifiable condition satisfied by a large class of directed acyclic graphs that is sufficient for balancedness of the associated DAG-game. We introduce a network canonization process and prove various structural results for the core of canonized DAG-games. In particular, we characterize classes of coalitions that have a constant payoff in the core. In addition, we identify a subset of the coalitions that is sufficient to determine the core.

Object Details

• ISBN: 978-615-5447-33-4
• Language: Englisch

References and Relationships

• Bibliographic citation: Series: IEHAS Discussion Papers ; No. MT-DP - 2014/18

Classification and Topics

• Classification: Wirtschaft ; Cooperative Games
• Subject: cooperative game theory ; directed acyclic graphs ; core ; acyclic directed Steiner tree

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Sziklai, Balázs ; Solymosi, Tamás ; Fleiner, Tamás
• Event: Veröffentlichung
• (who): Hungarian Academy of Sciences, Institute of Economics, Centre for Economic and Regional Studies
• (where): Budapest
• (when): 2014

Further information

• Handle: http://hdl.handle.net/10419/108335
• Last update: 10.03.2025, 11:43 AM CET