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Some generalizations of Kajii’s theorem to games with infinitely many players

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  • Yang, Zhe

Abstract

In this paper, we first generalize Kajii’s (1992) result in Hausdorff topological vector spaces. Second, we prove the existence of the finite-coalition α−core for games with infinitely many players. Third, by strengthening some assumptions, we prove the nonemptiness of the weak α−core for games with infinitely many players, Finally, we also characterize the weak α−core by providing a coincidence of the weak α−core and the closed-coalition α−core.

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  • 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.
    • Handle: RePEc:eee:mateco:v:76:y:2018:i:c:p:131-135
    DOI: 10.1016/j.jmateco.2018.04.004
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    3. 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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    Cited by:

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    2. 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.
    3. 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.

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