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On the Core of Directed Acyclic Graph Games

Author

Listed:
  • Balázs Sziklai

    () (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

  • Tamás Fleiner

    () (Department of Computer Science and Information Theory, Budapest University of Technology and Economics)

  • Tamás Solymosi

    () (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

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.

Suggested Citation

  • Balázs Sziklai & Tamás Fleiner & Tamás Solymosi, 2014. "On the Core of Directed Acyclic Graph Games," CERS-IE WORKING PAPERS 1418, Institute of Economics, Centre for Economic and Regional Studies.
  • Handle: RePEc:has:discpr:1418
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    References listed on IDEAS

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    More about this item

    Keywords

    cooperative game theory; directed acyclic graphs; core; acyclic directed Steiner tree;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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