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Some generalizations of Zhao’s theorem: Hybrid solutions and weak hybrid solutions for games with nonordered preferences

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  • Yang, Zhe
  • Yuan, George Xianzhi

Abstract

Inspired by Zhao (1992), we first define the hybrid solution of games with nonordered preferences and prove its existence theorem in Hausdorff topological vector spaces. Second, we introduce the open graph L-majorized condition for games with nonordered preferences. We shall provide an existence theorem of hybrid solutions for open graph L-majorized games. Third, we introduce the notion of weak hybrid solutions for games with infinitely many players. By strengthening some assumptions, we also obtain the existence theorem of weak hybrid solutions for games with infinitely many players.

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  • 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.
    • Handle: RePEc:eee:mateco:v:84:y:2019:i:c:p:94-100
    DOI: 10.1016/j.jmateco.2019.07.007
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    Cited by:

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    2. Bertrand Crettez & Rabia Nessah & Tarik Tazdaït, 2023. "On the strong $$\beta$$ β -hybrid solution of an N-person game," Theory and Decision, Springer, vol. 94(3), pages 363-377, April.
    3. Pendharkar, Parag C., 2021. "Allocating fixed costs using multi-coalition epsilon equilibrium," International Journal of Production Economics, Elsevier, vol. 239(C).
    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. 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.
    6. Bertrand Crettez & Rabia Nessah & Tarik Tazdaït, 2023. "On The Strong Β-Hybrid Solution Of An N-Person Game," Post-Print hal-04204632, HAL.

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