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Core stability in chain-component additive games

Author Info

  • 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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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Find related papers by JEL classification:
  • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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  1. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185.
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  3. 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.
  4. Le Breton, M. & Owen, G. & Weber, S., 1991. "Strongly Balanced Cooperative Games," G.R.E.Q.A.M. 91a09, Universite Aix-Marseille III.
  5. 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.
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  7. repec:dgr:kubcen:1999110 is not listed on IDEAS
  8. 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, School of Economics and Management.
  9. Amit K. Biswas & G. Ravindran & T. Parthasarathy, 2000. "Stability and largeness of core for symmetric games," International Journal of Game Theory, Springer, vol. 29(1), pages 11-22.
  10. 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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  12. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Other publications TiSEM cd695be5-0f54-4548-a952-2, School of Economics and Management.
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  14. Hamers, H.J.M. & Borm, P.E.M. & Tijs, S.H., 1995. "On games corresponding to sequencing situations with ready times," Other publications TiSEM 99882a33-06c1-4f7c-8436-6, School of Economics and Management.
  15. 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.
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Cited by:

  1. Csóka Péter & Herings P. Jean-Jacques & Kóczy László Á., 2007. "Balancedness Conditions for Exact Games," Research Memorandum 039, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. repec:spr:compst:v:78:y:2013:i:2:p:187-202 is not listed on IDEAS
  3. repec:spr:compst:v:74:y:2011:i:1:p:41-52 is not listed on IDEAS
  4. van Velzen, S., 2005. "Cooperation in Networks and Scheduling," Other publications TiSEM 81d927bb-fc40-4306-8f7f-a, School of Economics and Management.
  5. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer, vol. 78(2), pages 187-202, October.
  6. van Velzen, S., 2005. "Simple Combinatorial Optimisation Cost Games," Discussion Paper 2005-118, Tilburg University, Center for Economic Research.
  7. repec:dgr:kubcen:2005118 is not listed on IDEAS
  8. repec:dgr:uvatin:20110086 is not listed on IDEAS
  9. Estévez-Fernández, Arantza, 2012. "New characterizations for largeness of the core," Games and Economic Behavior, Elsevier, vol. 76(1), pages 160-180.
  10. repec:dgr:uvatin:2011086 is not listed on IDEAS
  11. repec:ner:tilbur:urn:nbn:nl:ui:12-170234 is not listed on IDEAS

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