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The average tree permission value for games with a permission tree

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  • van den Brink, J.R.

    (External organisation)

  • Herings, P.J.J.

    (General Economics 1 (Micro))

  • van der Laan, G.

    (Externe publicaties SBE)

  • Talman, A.J.J.

    (Externe publicaties SBE)

Abstract

In the literature various models of games with restricted cooperation can be found. In those models, instead of allowing for all subsets of the set of players to form, it is assumed that the set of feasible coalitions is a proper subset of the power set of the set of players. In this paper we consider such sets of feasible coalitions that follow from a permission structure on the set of players, in which players need permission to cooperate with other players. We assume the permission structure to be an oriented tree. This means that there is one player at the top of the permission structure and for every other player there is a unique directed path from the top player to this player. We introduce a new solution for these games based on the idea of the Average Tree value for cycle-free communication graph games. We provide two axiomatizations for this new value and compare it with the conjunctive permission value.

Suggested Citation

  • van den Brink, J.R. & Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2013. "The average tree permission value for games with a permission tree," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2013001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. René van den Brink, 2017. "Games with a Permission Structure: a survey on generalizations and applications," Tinbergen Institute Discussion Papers 17-016/II, Tinbergen Institute.
    2. M. Álvarez-Mozos & R. Brink & G. Laan & O. Tejada, 2017. "From hierarchies to levels: new solutions for games with hierarchical structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1089-1113, November.
    3. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2015. "Characterization of the Average Tree solution and its kernel," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 159-165.
    4. repec:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-017-0443-6 is not listed on IDEAS
    5. Mikel Álvarez-Mozos & René van den Brink & Gerard van der Laan & Oriol Tejada, 2015. "From Hierarchies to Levels: New Solutions for Games," Tinbergen Institute Discussion Papers 15-072/II, Tinbergen Institute.
    6. René Brink & Chris Dietz & Gerard Laan & Genjiu Xu, 2017. "Comparable characterizations of four solutions for permission tree games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 903-923, April.
    7. repec:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-017-0440-9 is not listed on IDEAS
    8. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
    9. Anna Khmelnitskaya & Gerard van der Laan & Dolf Talman, 2016. "Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games," Tinbergen Institute Discussion Papers 16-070/II, Tinbergen Institute.
    10. Suzuki, T., 2015. "Solutions for cooperative games with and without transferable utility," Other publications TiSEM 9bd876f2-c055-4d01-95f0-c, Tilburg University, School of Economics and Management.
    11. Takayuki Oishi & Gerard van der Laan & René van den Brink, 2016. "An Axiomatic Analysis of Joint Liability Problems with Rooted -Tree Structure," Tinbergen Institute Discussion Papers 16-042/II, Tinbergen Institute.

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    JEL classification:

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

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