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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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 62 (2008)
Issue (Month): 1 (January)
Pages: 116-139

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Handle: RePEc:eee:gamebe:v:62:y:2008:i:1:p:116-139

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Hamers, H.J.M. & Klijn, F. & Solymosi, T. & Tijs, S.H. & Vermeulen, D., 1999. "On the Nucleolus of Neighbour Games," Discussion Paper 1999-111, Tilburg University, Center for Economic Research.
  2. Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991. "Strongly balanced cooperative games," Discussion Paper Serie A 338, University of Bonn, Germany.
  3. Hamers, H. & Borm, P. & Tijs, S., 1993. "A Games Corresponding to Sequencing Situations with Ready Times," Papers 9316, Tilburg - Center for Economic Research.
  4. J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer, vol. 28(2), pages 211-227.
  5. Klijn, F. & Vermeulen, D. & Hamers, H.J.M. & Solymosi, T. & Tijs, S.H. & Pere Villar, J., 1999. "Neighbour Games and the Leximax Solution," Discussion Paper 1999-110, Tilburg University, Center for Economic Research.
  6. Potters, Jos & Reijnierse, Hans, 1995. "Gamma-Component Additive Games," International Journal of Game Theory, Springer, vol. 24(1), pages 49-56.
  7. Hamers, H.J.M. & Klijn, F. & Velzen, S. van, 2002. "On the Convexity of Precedence Sequencing Games," Discussion Paper 2002-112, Tilburg University, Center for Economic Research.
  8. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
  9. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154192, Tilburg University.
  10. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185.
  11. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154243, Tilburg University.
  12. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
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Cited by:
  1. Arantza Estevez-Fernandez, 2011. "New Characterizations for Largeness of the Core," Tinbergen Institute Discussion Papers 11-086/1, Tinbergen Institute.
  2. Velzen, S. van, 2005. "Simple Combinatorial Optimisation Cost Games," Discussion Paper 2005-118, Tilburg University, Center for Economic Research.
  3. Velzen, S. van, 2005. "Cooperation in Networks and Scheduling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-170234, Tilburg University.

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