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Core stability in chain-component additive games

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Author Info
Velzen, S. van
Hamers, H.J.M.
Solymosi, T. (Tilburg University, Center for Economic Research)

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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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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 101.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:2004101

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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hamers, H. & Klijn, F. & Solymosi, T., 1999. "On the nucleolus of neighbour games," Discussion Paper 111, Tilburg University, Center for Economic Research. [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  5. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185. [Downloadable!] (restricted)
  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. & Klijn, P. & Velzen, B. van, 2002. "On the convexity of precedence sequencing games," Discussion Paper 112, Tilburg University, Center for Economic Research. [Downloadable!]
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  1. Velzen, Bas van, 2005. "Simple combinatorial optimisation cost games," Discussion Paper 118, Tilburg University, Center for Economic Research. [Downloadable!]
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