On the Core of Directed Acyclic Graph Games - Balázs Sziklai; Tamás Solymosi; Tamás Fleiner (Hungarian Academy of Sciences, Institute of Economics, Centre for Economic and Regional Studies, 2014)
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.
Keywords: C71; 330; cooperative game theory; directed acyclic graphs; core; acyclic directed Steiner tree