Journal of the Operations Research Society of China ›› 2025, Vol. 13 ›› Issue (2): 660-670.doi: 10.1007/s40305-023-00497-x

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The mixed-strategy α-core of games with infinitely many pure strategies

Neng-Fa Wang1,2, Zhe Yang3,4   

  1. 1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China;
    2. Guizhou Key Laboratory of Big Data Statistical Analysis, Guiyang 550025, Guizhou, China;
    3. School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China;
    4. Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai 200433, China
  • Received:2022-07-07 Revised:2023-05-27 Online:2025-06-30 Published:2025-07-07
  • Contact: Neng-Fa Wang E-mail:nengfa_wang@163.com
  • Supported by:
    This research was supported by the Innovation Exploration and Academic New Seedling Project of Guizhou University of Finance and Economics (No. 2022XSXMB22) and Guizhou Key Laboratory of Big Data Statistical Analysis (No. [2019]5103).

Abstract: Inspired by Scarf (J Econ Theory 3:169–181, 1971) and Kajii (J Econ Theory 56:194–205, 1992), we introduce the notion of mixed-strategy α-core for games with infinitely many pure strategies. We first show the nonemptiness of the mixed-strategy α-core for normal-form games with infinitely many pure strategies and obtain the generic continuity property of the mixed-strategy α-core correspondence. Furthermore, we prove the existence of the mixed-strategy α-core for games with nonordered preferences and infinitely many pure strategies and show the generic continuity property of the mixed-strategy α-core correspondence.

Key words: Games with infinitely many pure strategies, Mixed-strategy α-core, Existence, Generic continuity

CLC Number: