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The mixed-strategy \(\alpha \)-core of games with infinitely many pure strategies

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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 \(\alpha \)-core for games with infinitely many pure strategies. We first show the nonemptiness of the mixed-strategy \(\alpha \)-core for normal-form games with infinitely many pure strategies and obtain the generic continuity property of the mixed-strategy \(\alpha \)-core correspondence. Furthermore, we prove the existence of the mixed-strategy \(\alpha \)-core for games with nonordered preferences and infinitely many pure strategies and show the generic continuity property of the mixed-strategy \(\alpha \)-core correspondence.

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Acknowledgements

The authors gratefully acknowledge the two anonymous reviewers for their constructive comments and valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, Guizhou, China

    Neng-Fa Wang

  2. Guizhou Key Laboratory of Big Data Statistical Analysis, Guiyang, 550025, Guizhou, China

    Neng-Fa Wang

  3. School of Economics, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Zhe Yang

  4. Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai, 200433, China

    Zhe Yang

Authors
  1. Neng-Fa Wang
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  2. Zhe Yang
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Contributions

The authors contributed equally to this work. Both authors have read and approved the final manuscript.

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Correspondence to Neng-Fa Wang.

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The authors declare that they have no conflict of interest.

Additional information

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).

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Wang, NF., Yang, Z. The mixed-strategy \(\alpha \)-core of games with infinitely many pure strategies. J. Oper. Res. Soc. China (2023). https://doi.org/10.1007/s40305-023-00497-x

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  • DOI: https://doi.org/10.1007/s40305-023-00497-x

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