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The Maximal Payoff and Coalition Formation in Coalitional Games

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  • Zhao, Jingang

Abstract

This paper first establishes a new core theorem using the concept of generated payoffs: the TU (transferable utility) core is empty if and only if the maximum of generated payoffs (mgp) is greater than the grand coalition’s payoff v(N), or if and only if it is irrational to split v(N). It then provides answers to the questions of what payoffs to split, how to split the payoff, what coalitions to form, and how long each of the coalitions will be formed by rational players in coalitional TU games. Finally, it obtains analogous results in coalitional NTU (non-transferable utility) games.

Suggested Citation

  • Zhao, Jingang, 2008. "The Maximal Payoff and Coalition Formation in Coalitional Games," Coalition Theory Network Working Papers 6298, Fondazione Eni Enrico Mattei (FEEM).
    • Handle: RePEc:ags:feemct:6298
    DOI: 10.22004/ag.econ.6298
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    References listed on IDEAS

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    1. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    2. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    3. Jingang Zhao, 2001. "The relative interior of the base polyhedron and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 635-648.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    6. Kannai, Yakar, 1992. "The core and balancedness," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 12, pages 355-395, Elsevier.
    7. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
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    Cited by:

    1. Juan C. Cesco, 2012. "Nonempty Core-Type Solutions Over Balanced Coalitions In Tu-Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1-16.

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    More about this item

    Keywords

    Institutional and Behavioral Economics; Research Methods/ Statistical Methods;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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