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A Note on the Core of TU-cooperative Games with Multiple Membership Externalities

Author

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  • Heinrich H. Nax

    (Department of Social Sciences, ETH Zürich, Clausiusstrasse 37-C3, Zürich 8092, Switzerland)

Abstract

A generalization of transferable utility cooperative games from the functional forms introduced by von Neumann and Morgenstern (1944, Theory of Games and Economic Behavior) and Lucas and Thrall (1963, Naval Research Logistics Quarterly, 10, 281–298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for the cross-cutting of contractual arrangements are illustrated and discussed.

Suggested Citation

  • Heinrich H. Nax, 2014. "A Note on the Core of TU-cooperative Games with Multiple Membership Externalities," Games, MDPI, vol. 5(4), pages 1-13, October.
    • Handle: RePEc:gam:jgames:v:5:y:2014:i:4:p:191-203:d:41422
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    References listed on IDEAS

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    1. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    2. Effrosyni Diamantoudi & Inés Macho-Stadler & David Pérez-Castrillo & Licun Xue, 2015. "Sharing the surplus in games with externalities within and across issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 315-343, October.
    3. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, vol. 26(2), pages 286-336, January.
    4. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    5. Bloch, Francis & van den Nouweland, Anne, 2014. "Expectation formation rules and the core of partition function games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 339-353.
    6. R. M. Thrall & W. F. Lucas, 1963. "N‐person games in partition function form," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 281-298, March.
    7. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    8. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
    9. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    10. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
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    Cited by:

    1. Effrosyni Diamantoudi & Inés Macho-Stadler & David Pérez-Castrillo & Licun Xue, 2015. "Sharing the surplus in games with externalities within and across issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 315-343, October.
    2. Giorgos Stamatopoulos, 2020. "On the $$\gamma $$γ-core of asymmetric aggregative games," Theory and Decision, Springer, vol. 88(4), pages 493-504, May.
    3. Hirbod Assa & Sheridon Elliston & Ehud Lehrer, 2016. "Joint games and compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 91-113, January.
    4. Messan Agbaglah, 2017. "Overlapping coalitions, bargaining and networks," Theory and Decision, Springer, vol. 82(3), pages 435-459, March.
    5. Gayer, Gabrielle & Persitz, Dotan, 2016. "Negotiation across multiple issues," Theoretical Economics, Econometric Society, vol. 11(3), September.
    6. Sokolov, Denis, 2022. "Shapley value for TU-games with multiple memberships and externalities," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 76-90.
    7. Stamatopoulos, Giorgos, 2018. "On the gamma-core of asymmetric aggregative games," MPRA Paper 88722, University Library of Munich, Germany.
    8. Stamatopoulos, Giorgos, 2018. "Cooperative games with externalities and probabilistic coalitional beliefs," MPRA Paper 92862, University Library of Munich, Germany.

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