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The weak-core of a game in normal form with a continuum of players

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  • Youcef Askoura

    (LEMMA - Laboratoire d'économie mathématique et de microéconomie appliquée - UP2 - Université Panthéon-Assas)

Abstract

This paper deals with the weak-core of normal form games with a continuum set of players and without side payments. This concept is an approximation of the core introduced by Weber, Shapley and Shubik. The weak-core is slightly larger than Aumann's α−core when adapted to large anonymous games. A non emptiness result is obtained based on the well known Scarf's non vacuity theorem for finite games.

Suggested Citation

  • Youcef Askoura, 2011. "The weak-core of a game in normal form with a continuum of players," Post-Print hal-01982380, HAL.
    • Handle: RePEc:hal:journl:hal-01982380
    DOI: 10.1016/j.jmateco.2010.11.003
    Note: View the original document on HAL open archive server: https://hal.science/hal-01982380
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    References listed on IDEAS

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    15. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 427-433, July.
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    Cited by:

    1. Yang, Zhe, 2017. "Some infinite-player generalizations of Scarf’s theorem: Finite-coalition α-cores and weak α-cores," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 81-85.
    2. Youcef Askoura, 2019. "On the core of normal form games with a continuum of players : a correction," Papers 1903.09819, arXiv.org.
    3. Zhe Yang & Haiqun Zhang, 2019. "NTU core, TU core and strong equilibria of coalitional population games with infinitely many pure strategies," Theory and Decision, Springer, vol. 87(2), pages 155-170, September.
    4. Askoura, Y., 2017. "On the core of normal form games with a continuum of players," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 32-42.
    5. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    6. Yang, Zhe, 2018. "Some generalizations of Kajii’s theorem to games with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 131-135.
    7. Yang, Zhe & Zhang, Xian, 2021. "A weak α-core existence theorem of games with nonordered preferences and a continuum of agents," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    8. Yang, Zhe & Yuan, George Xianzhi, 2019. "Some generalizations of Zhao’s theorem: Hybrid solutions and weak hybrid solutions for games with nonordered preferences," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 94-100.
    9. Yang, Zhe, 2020. "The weak α-core of exchange economies with a continuum of players and pseudo-utilities," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 43-50.
    10. Lan Di & George X. Yuan & Tu Zeng, 2021. "The consensus equilibria of mining gap games related to the stability of Blockchain Ecosystems," The European Journal of Finance, Taylor & Francis Journals, vol. 27(4-5), pages 419-440, March.
    11. Jian Yang, 2023. "Partition-based Stability of Coalitional Games," Papers 2304.10651, arXiv.org.

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