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Alpha cores of games with nonatomic asymmetric information

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  • Noguchi, Mitsunori

Abstract

In this paper, we ask under what reasonable conditions a game with asymmetric information on a continuum of states admits a non-empty α-core. Players examine various private information-constrained contracts f (pure strategy profiles) for ex-ante efficiency by evaluating ex-ante expected payoffs and by forming ex-ante coalitions. Once the players agree on a contract, they implement it faithfully in the interim stage. Roughly speaking, our conclusion states that if players hold fine (non-atomic) and independent information, there exists an ex-ante efficient set of contracts (an ex-ante α-core pure strategy profile) that is implementable in the interim stage. To prove that α-cores are non-empty, we need a variant of Lyapunov’s theorem for Young measures that preserves private information. We apply an iterated integral version of Lyapunov’s theorem for Young measures to derive such a variant.

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  • Noguchi, Mitsunori, 2018. "Alpha cores of games with nonatomic asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 1-12.
    • Handle: RePEc:eee:mateco:v:75:y:2018:i:c:p:1-12
    DOI: 10.1016/j.jmateco.2017.12.005
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    Cited by:

    1. 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.
    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. Fukuda, Satoshi, 2019. "Epistemic foundations for set-algebraic representations of knowledge," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 73-82.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    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.

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