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Some infinite-player generalizations of Scarf’s theorem: Finite-coalition α-cores and weak α-cores

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  • Yang, Zhe

Abstract

In this paper, we first obtain some infinite-dimension versions of Scarf’s theorem. Second, we provide two generalizations of Scarf (1971) to normal-form games with infinitely many players. Under the assumptions analogous to Scarf (1971), we prove the nonemptiness of the finite-coalition α-core. Furthermore, by strengthening the assumptions, we obtain the nonemptiness of the weak α-core, and show that the weak α-core coincides with the closed-coalition α-core.

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  • 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.
    • Handle: RePEc:eee:mateco:v:73:y:2017:i:c:p:81-85
    DOI: 10.1016/j.jmateco.2017.09.005
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    1. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
    2. Askoura, Y., 2015. "An interim core for normal form games and exchange economies with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 38-45.
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    8. Youcef Askoura, 2011. "The weak-core of a game in normal form with a continuum of players," Post-Print hal-01982380, HAL.
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    10. Askoura, Y. & Sbihi, M. & Tikobaini, H., 2013. "The ex ante α-core for normal form games with uncertainty," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 157-162.
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    Cited by:

    1. 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.
    2. 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.
    3. Ken Urai & Hiromi Murakami & Weiye Chen, 2023. "Generalization of the social coalitional equilibrium structure," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 1-25, April.

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