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Essential stability of $$\alpha $$ α -core

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  • Zhe Yang

    (Shanghai University of Finance and Economics
    Ministry of Education)

Abstract

Using the existence results in Kajii (J Econ Theory 56:194–205, 1992), we identify a class of n-person noncooperative games containing a dense residual subset of games whose cooperative equilibria are all essential. Moreover, we show that every game in this collection possesses an essential component of the $$\alpha $$ α -core by proving the connectivity of minimal essential subsets of the $$\alpha $$ α -core.

Suggested Citation

  • Zhe Yang, 2017. "Essential stability of $$\alpha $$ α -core," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 13-28, March.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-015-0515-5
    DOI: 10.1007/s00182-015-0515-5
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    References listed on IDEAS

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    1. Yong-Hui Zhou & Jian Yu & Shu-Wen Xiang, 2007. "Essential stability in games with infinitely many pure strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 493-503, April.
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    3. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    4. Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
    5. Al-Najjar, Nabil, 1995. "Strategically stable equilibria in games with infinitely many pure strategies," Mathematical Social Sciences, Elsevier, vol. 29(2), pages 151-164, April.
    6. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    7. Kajii, Atsushi, 1992. "A generalization of Scarf's theorem: An [alpha]-core existence theorem without transitivity or completeness," Journal of Economic Theory, Elsevier, vol. 56(1), pages 194-205, February.
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