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The non-emptiness of the core of a partition function form game

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  • Takaaki Abe

    (Waseda University)

  • Yukihiko Funaki

    (Waseda University)

Abstract

The purpose of this paper is to provide a necessary and sufficient condition for the non-emptiness of the core for partition function form games. We generalize the Bondareva–Shapley condition to partition function form games and present the condition for the non-emptiness of “the pessimistic core”, and “the optimistic core”. The pessimistic (optimistic) core describes the stability in assuming that players in a deviating coalition anticipate the worst (best) reaction from the other players. In addition, we define two other notions of the core based on exogenous partitions. The balanced collections in partition function form games and some economic applications are also provided.

Suggested Citation

  • Takaaki Abe & Yukihiko Funaki, 2017. "The non-emptiness of the core of a partition function form game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 715-736, August.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0554-6
    DOI: 10.1007/s00182-016-0554-6
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    References listed on IDEAS

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    1. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, vol. 26(2), pages 286-336, January.
    2. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    3. László Kóczy, 2007. "A recursive core for partition function form games," Theory and Decision, Springer, vol. 63(1), pages 41-51, August.
    4. 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.
    5. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    6. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 157-171.
    7. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
    8. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 185-187.
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    Citations

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    Cited by:

    1. Takaaki Abe, 2020. "Stable Coalition Structures and Power Indices for Majority Voting," Working Papers 2015, Waseda University, Faculty of Political Science and Economics.
    2. Yang, Guangjing & Sun, Hao, 2023. "The recursive nucleolus for partition function form games," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    3. Yang, Guangjing & Sun, Hao & Hou, Dongshuang & Xu, Genjiu, 2019. "Games in sequencing situations with externalities," European Journal of Operational Research, Elsevier, vol. 278(2), pages 699-708.
    4. Takaaki Abe, 2019. "Cartel formation in Cournot competition with asymmetric costs: A partition function approach," Working Papers 1911, Waseda University, Faculty of Political Science and Economics.
    5. Takaaki Abe, 2020. "Population monotonic allocation schemes for games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 97-117, March.
    6. Takaaki Abe, 2021. "Cartel Formation in Cournot Competition with Asymmetric Costs: A Partition Function Approach," Games, MDPI, vol. 12(1), pages 1-16, February.
    7. Techer, Kevin, 2021. "Stable agreements through liability rules: A multi-choice game approach to the social cost problem," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 77-88.
    8. Takaaki Abe & Yukihiko Funaki, 2021. "The projective core of symmetric games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 167-183, March.
    9. Takaaki Abe & Yukihiko Funaki, 2018. "The Unbinding Core for Coalitional Form Games," Working Papers 1805, Waseda University, Faculty of Political Science and Economics.
    10. Subhadip Chakrabarti & Robert P. Gilles & Emiliya Lazarova, 2021. "Stability of cartels in Multimarket Cournot oligopolies," Manchester School, University of Manchester, vol. 89(1), pages 70-85, January.
    11. Takaaki Abe, 2018. "Stable coalition structures in symmetric majority games: a coincidence between myopia and farsightedness," Theory and Decision, Springer, vol. 85(3), pages 353-374, October.
    12. Abe, Takaaki, 2019. "Decomposing a balanced game: A necessary and sufficient condition for the nonemptiness of the core," Economics Letters, Elsevier, vol. 176(C), pages 9-13.
    13. Aivazian, Varouj A. & Callen, Jeffrey L., 2023. "The Coase Theorem and the empty core: Inspecting the entrails after four decades," International Review of Law and Economics, Elsevier, vol. 73(C).

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