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Cooperative Games in Graph Structure

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  • Herings, P.J.J.

    (Tilburg University, Center For Economic Research)

  • van der Laan, G.
  • Talman, A.J.J.

    (Tilburg University, Center For Economic Research)

Abstract

In this paper we generalize the concept of coalitional games by allowingfor any organizational structure within coalitions represented by a graphon the set of players ot the coalition. A, possibly empty, set of payoffvectors is assigned to any graph on every subset of players. Such a gamewill be called a graph game. For each graph a power vector is determinedthat depends on the relative positions of the players within the graph.A collection of graphs will be called balanced if to any graph in the collection apositive weight can be assigned such that the weighted power vectorssum up to the vector of ones. We then define the balanced-core as a refinement ofthe core. A payoff vector lies in the balanced-core if it lies in the core andthe payoff vector is an element of payoff sets of all graphs in some balanced collection ofgraphs. We prove that any balanced graph game has a nonempty balanced-core.We conclude by some examples showing the usefulness of the conceptsof graph games and balanced-core. In particular these examples show a closerelationship between solutions to noncooperative games andbalanced-core elements of a well-defined graph game.
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  • Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2000. "Cooperative Games in Graph Structure," Discussion Paper 2000-90, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:bab30745-01b4-480b-a8ac-48a347ed9d9d
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    References listed on IDEAS

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    1. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2001. "Measuring the Power of Nodes in Digraphs," Other publications TiSEM 8ad1bdb1-a602-4674-b737-2, Tilburg University, School of Economics and Management.
    2. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.

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    cooperative games; graphs;

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