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Existence and stability of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader–follower games

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Abstract

In this paper, we mainly study a kind of generalized multiobjective multi-leader–follower games in Hausdorff topological spaces. We establish an existence theorem of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader–follower games. As a special case, we also obtain a sufficient condition on the existence theorem of Nash equilibrium for single-leader–multi-follower games. Moreover, we deduce some results on the generic stability of generalized multiobjective multi-leader–follower games by using the method of essential solutions.

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Acknowledgments

The authors would like to thank the editor and two anonymous referees for their helpful comments and valuable suggestions which improved the original manuscript greatly. This work was supported by the National Natural Science Foundation of China (No. 11161008), Doctoral Program Fund for Ministry of Education (No. 20115201110002) and Natural Science Fund of Guizhou Province (No. 20122139).

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Authors and Affiliations

  1. College of Computer Science, Guizhou University, Guiyang , 550025, Guizhou, China

    Wensheng Jia & Yanlong Yang

  2. College of Science, Guizhou University, Guiyang , 550025, Guizhou, China

    Wensheng Jia, Shuwen Xiang & Jihao He

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  1. Wensheng Jia
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  2. Shuwen Xiang
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  3. Jihao He
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  4. Yanlong Yang
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Correspondence to Shuwen Xiang.

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Jia, W., Xiang, S., He, J. et al. Existence and stability of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader–follower games. J Glob Optim 61, 397–405 (2015). https://doi.org/10.1007/s10898-014-0178-y

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  • DOI: https://doi.org/10.1007/s10898-014-0178-y

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