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Core stability in chain-component additive games

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  • van Velzen, Bas
  • Hamers, Herbert
  • Solymosi, Tamas

Abstract

Chain-component additive games are graph-restricted superadditive games, where an exogenously given line-graph determines the cooperative possibilities of the players.These games can model various multi-agent decision situations, such as strictly hierarchical organisations or sequencing / scheduling related problems, where an order of the agents is fixed by some external factor, and with respect to this order only consecutive coalitions can generate added value. In this paper we characterise core stability of chain-component additive games in terms of polynomial many linear inequalities and equalities that arise from the combinatorial structure of the game.Furthermore we show that core stability is equivalent to essential extendibility.We also obtain that largeness of the core as well as extendibility and exactness of the game are equivalent properties which are all sufficient for core stability.Moreover, we also characterise these properties in terms of linear inequalities.
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Suggested Citation

  • van Velzen, Bas & Hamers, Herbert & Solymosi, Tamas, 2008. "Core stability in chain-component additive games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 116-139, January.
  • Handle: RePEc:eee:gamebe:v:62:y:2008:i:1:p:116-139
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    1. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Other publications TiSEM be67f9e9-7a4a-47f1-9fb9-7, Tilburg University, School of Economics and Management.
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    5. J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 211-227.
    6. Tamás Solymosi & Harry Aarts & Theo Driessen, 1998. "On Computing the Nucleolus of a Balanced Connected Game," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 983-1009, November.
    7. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Other publications TiSEM cd695be5-0f54-4548-a952-2, Tilburg University, School of Economics and Management.
    8. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Vermeulen, Dries, 2003. "On the nucleolus of neighbor games," European Journal of Operational Research, Elsevier, vol. 146(1), pages 1-18, April.
    9. Flip Klijn & Dries Vermeulen & Herbert Hamers & Tamás Solymosi & Stef Tijs & Joan Pere Villar, 2003. "Neighbor games and the leximax solution," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 191-208, November.
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    12. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
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    Cited by:

    1. Péter Csóka & P. Herings & László Kóczy, 2011. "Balancedness conditions for exact games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 41-52, August.
    2. Estévez-Fernández, Arantza, 2012. "New characterizations for largeness of the core," Games and Economic Behavior, Elsevier, vol. 76(1), pages 160-180.
    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    4. van Velzen, S., 2005. "Simple Combinatorial Optimisation Cost Games," Discussion Paper 2005-118, Tilburg University, Center for Economic Research.
    5. van Velzen, S., 2005. "Cooperation in Networks and Scheduling," Other publications TiSEM 81d927bb-fc40-4306-8f7f-a, Tilburg University, School of Economics and Management.
    6. repec:spr:compst:v:78:y:2013:i:2:p:187-202 is not listed on IDEAS
    7. repec:spr:compst:v:74:y:2011:i:1:p:41-52 is not listed on IDEAS

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    JEL classification:

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

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