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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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    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. 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.
    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.
    4. Martins-da-Rocha, Victor Filipe & Yannelis, Nicholas C., 2011. "Non-emptiness of the alpha-core," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 716, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    5. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-1350, November.
    6. Askoura, Y., 2011. "The weak-core of a game in normal form with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 43-47, January.
    7. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    8. Hildenbrand, Werner & Schmeidler, David & Zamir, Shmuel, 1973. "Existence of Approximate Equilibria and Cores," Econometrica, Econometric Society, vol. 41(6), pages 1159-1166, November.
    9. Youcef Askoura, 2011. "The weak-core of a game in normal form with a continuum of players," Post-Print hal-01982380, HAL.
    10. Weber, S., 1981. "Some results on the weak core of a non-side-payment game with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 101-111, March.
    11. 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.
    12. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 245-258.
    13. 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.
    14. Noguchi, Mitsunori, 2018. "Alpha cores of games with nonatomic asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 1-12.
    15. Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies," Journal of Economic Theory, Elsevier, vol. 49(1), pages 135-168, October.
    16. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    17. Noguchi, Mitsunori, 2014. "Cooperative equilibria of finite games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 4-10.
    18. Hammond, Peter J. & Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "Continuum economies with finite coalitions: Core, equilibria, and widespread externalities," Journal of Economic Theory, Elsevier, vol. 49(1), pages 113-134, October.
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    Cited by:

    1. 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.
    2. Crettez, Bertrand & Nessah, Rabia & Tazdaït, Tarik, 2022. "On the strong hybrid solution of an n-person game," Mathematical Social Sciences, Elsevier, vol. 117(C), pages 61-68.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. Wang, Lei & Zhao, Jingang, 2024. "The core in an N-firm dynamic Cournot oligopoly," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 20-26.

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