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Essential stability in games with endogenous sharing rules

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  • Zhou, Yong-Hui
  • Yu, Jian
  • Xiang, Shu-Wen
  • Wang, Long

Abstract

We prove that essential games with endogenous sharing rules form a dense residual set and that every game with endogenous sharing rules has at least one minimal essential set of solutions. Furthermore, we establish that essential continuous games form a dense residual set and that every continuous game has at least one minimal essential set of Nash equilibria.

Suggested Citation

  • Zhou, Yong-Hui & Yu, Jian & Xiang, Shu-Wen & Wang, Long, 2009. "Essential stability in games with endogenous sharing rules," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 233-240, March.
    • Handle: RePEc:eee:mateco:v:45:y:2009:i:3-4:p:233-240
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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.
    2. 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.
    3. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    4. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    5. Q. Luo, 1999. "Essential Component and Essential Optimum Solution of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 433-438, August.
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