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Games with a Permission Structure: a survey on generalizations and applications

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  • René van den Brink

    (VU University Amsterdam, The Netherlands)

Abstract

In the field of cooperative games with restricted cooperation, various restrictions on coalition formation are studied. The most studied restrictions are those that arise from restricted communication and hierarchies. This survey discusses several models of hierarchy restrictions and their relation with communication restrictions. In the literature, there are results on game properties, Harsanyi dividends, core stability, and various solutions that generalize exisiting solutions for TU-games. In this survey we mainly focus on axiomatizations of the Shapley value in different models of games with a hierarchically structured player set, and their applications. Not only do these axiomatizations provide insight in the Shapley value for these models, but also by considering the types of axioms that characterize the Shapley value, we learn more about different network structures. A central model of games with hierarchies are the games with a permission structure where players in a cooperative transferable utility game are part of a permission structure in the sense that there are players that need permission from other players before they are allowed to cooperate. This permission structure is represented by a directed graph. Generalizations of this model are, for example, games on antimatroids, and games with a local permission structure. Besides discussing these generalizations, we briefly discuss some applications, in particular auction games and hierarchically structured firms.

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20170016
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    References listed on IDEAS

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    1. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
    2. René Brink & Chris Dietz, 2014. "Games with a local permission structure: separation of authority and value generation," Theory and Decision, Springer, vol. 76(3), pages 343-361, March.
    3. Lange, Fabien & Grabisch, Michel, 2009. "Values on regular games under Kirchhoff's laws," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 322-340, November.
    4. Rodica Brânzei & Vito Fragnelli & Stef Tijs, 2002. "Tree-connected peer group situations and peer group games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 93-106, March.
    5. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    6. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, September.
    7. René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 175-188, May.
    8. René Brink & Ilya Katsev & Gerard Laan, 2011. "A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 591-616, August.
    9. Endre Bjørndal & Herbert Hamers & Maurice Koster, 2004. "Cost allocation in a bank ATM network," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 405-418, July.
    10. van den Brink, René & Katsev, Ilya & van der Laan, Gerard, 2010. "An algorithm for computing the nucleolus of disjunctive non-negative additive games with an acyclic permission structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 817-826, December.
    11. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, July.
    12. Pieter H.M. Ruys & René van den Brink & Radislav Semenov, 2000. "Values and governance systems," Chapters, in: Claude Ménard (ed.), Institutions, Contracts and Organizations, chapter 27, Edward Elgar Publishing.
    13. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2001. "The Myerson value for union stable structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 359-371, December.
    14. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    15. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    16. Matthew O. Jackson & Tomas Rodriguez-Barraquer & Xu Tan, 2012. "Social Capital and Social Quilts: Network Patterns of Favor Exchange," American Economic Review, American Economic Association, vol. 102(5), pages 1857-1897, August.
    17. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    18. Claude Ménard (ed.), 2000. "Institutions, Contracts and Organizations," Books, Edward Elgar Publishing, number 1921.
    19. Baomin Dong & Debing Ni & Yuntong Wang, 2012. "Sharing a Polluted River Network," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 53(3), pages 367-387, November.
    20. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    21. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
    22. Marcin Malawski, 2002. "Equal treatment, symmetry and Banzhaf value axiomatizations," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 47-67.
    23. René Brink, 2010. "Axiomatizations of Banzhaf permission values for games with a permission structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 445-466, July.
    24. Bilbao, J.M. & Ordóñez, M., 2009. "Axiomatizations of the Shapley value for games on augmenting systems," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1008-1014, August.
    25. Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, vol. 60(1), pages 176-186, July.
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    Citations

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    Cited by:

    1. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2022. "The priority value for cooperative games with a priority structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 431-450, June.
    2. Béal, Sylvain & Moyouwou, Issofa & Rémila, Eric & Solal, Philippe, 2020. "Cooperative games on intersection closed systems and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 15-22.
    3. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    4. David Lowing, 2023. "Allocation rules for multi-choice games with a permission tree structure," Annals of Operations Research, Springer, vol. 320(1), pages 261-291, January.
    5. Tobias Hiller, 2021. "Hierarchy and the size of a firm," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 68(3), pages 389-404, September.
    6. Sylvain Béal & Issofa Moyouwou & Eric Rémila & Phillippe Solal, 2018. "Cooperative games on intersection closed systems and the Shapley value," Working Papers 2018-06, CRESE.
    7. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2023. "Properties of Solutions for Games on Union-Closed Systems," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    8. Juan Vidal-Puga, 2017. "Comments on: Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 42-44, April.

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    More about this item

    Keywords

    Cooperative TU-game; hierarchy; permission structure; antimatroid; local permission structure; applications.;
    All these keywords.

    JEL classification:

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

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