On the Core of Directed Acyclic Graph Games

Balázs Sziklai, Tamás Fleiner () and Tamás Solymosi
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Tamás Fleiner: Department of Computer Science and Information Theory, Budapest University of Technology and Economics

No 1418, CERS-IE WORKING PAPERS from Institute of Economics, Centre for Economic and Regional Studies

Abstract: 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: cooperative game theory; directed acyclic graphs; core; acyclic directed Steiner tree (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2014-07
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-net
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