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On Existence of alpha-Core Solutions for Games with Finite or Infinite Players

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  • Qi-Qing Song
  • Min Guo

Abstract

This gives two existence results of alpha-core solutions by introducing P-open conditions and strong P-open conditions into games without ordered preferences. The existence of alpha-core solutions is obtained for games with infinite-players. Secondly, it provides a short proof of Kajii's (Journal of Economic Theory 56, 194-205, 1992) existence theorem for alpha-core solutions, further, the Kajii's theorem is equivalent to the Browder fixed point theorem. In addition, the obtained existence results can include many typical results for alpha-core solutions and some recent existence results as special cases.

Suggested Citation

  • Qi-Qing Song & Min Guo, 2022. "On Existence of alpha-Core Solutions for Games with Finite or Infinite Players," Papers 2211.03112, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:2211.03112
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    References listed on IDEAS

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    1. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    2. Weber, S., 1981. "Some results on the weak core of a non-side-payment game with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 101-111, March.
    3. Zhao, Jingang, 1992. "The hybrid solutions of an N-person game," Games and Economic Behavior, Elsevier, vol. 4(1), pages 145-160, January.
    4. Liu, Jiuqiang & Liu, Xiaodong, 2013. "A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 150-156.
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