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The ex ante α-core for normal form games with uncertainty

Author

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  • Youcef Askoura

    (Chercheur indépendant)

  • Mohammed Sbihi

    (MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien - ENAC - Ecole Nationale de l'Aviation Civile)

  • Hamid Tikobaini

    (LMPA - Laboratoire de Mathématiques Pures et Appliquées [Tizi-Ouzou] - UMMTO - Université Mouloud Mammeri [Tizi Ouzou] = Mouloud Mammeri University of Tizi-Ouzou)

Abstract

In this paper we study the existence of the α-core for an n-person game with incomplete information. We follow a Milgrom-Weber-Balder formulation of a game with incomplete information. The players adopt behavioral strategies represented by Young measures. The game unrolls in one step at the ex ante stage. In this context, the mixed-extensions of the utility functions are not quasi-concave, and as a result the classical Scarf's theorem cannot be applied. An approximation argument is used to overcome this lack of concavity.

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  • Youcef Askoura & Mohammed Sbihi & Hamid Tikobaini, 2013. "The ex ante α-core for normal form games with uncertainty," Post-Print hal-00924267, HAL.
    • Handle: RePEc:hal:journl:hal-00924267
    DOI: 10.1016/j.jmateco.2013.01.007
    Note: View the original document on HAL open archive server: https://enac.hal.science/hal-00924267
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    References listed on IDEAS

    as
    1. Forges, Francoise & Minelli, Enrico & Vohra, Rajiv, 2002. "Incentives and the core of an exchange economy: a survey," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 1-41, September.
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    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. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    7. Myerson, Roger B., 2007. "Virtual utility and the core for games with incomplete information," Journal of Economic Theory, Elsevier, vol. 136(1), pages 260-285, September.
    8. Balder E. J. & Rustichini A., 1994. "An Equilibrium Result for Games with Private Information and Infinitely Many Players," Journal of Economic Theory, Elsevier, vol. 62(2), pages 385-393, April.
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    11. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
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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. Noguchi, Mitsunori, 2021. "Essential stability of the alpha cores of finite games with incomplete information," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 34-43.
    3. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    4. Noguchi, Mitsunori, 2014. "Cooperative equilibria of finite games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 4-10.
    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. Noguchi, Mitsunori, 2018. "Alpha cores of games with nonatomic asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 1-12.
    10. 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.
    11. Khan, M. Ali & Sagara, Nobusumi, 2016. "Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibria," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 95-107.
    12. Youcef Askoura, 2019. "An interim core for normal form games and exchange economies with incomplete information: a correction," Papers 1903.09867, arXiv.org.

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    More about this item

    Keywords

    α-core; game with incomplete information; normal form games; behavioral strategies; game with uncertainty;
    All these keywords.

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