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Some Relaxed Solutions of Minimax Inequality for Discontinuous Game

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Game Theory and Applications (China GTA 2016, China-Dutch GTA 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 758))

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Abstract

In this paper, we first prove the existence results of minimax inequality under some relaxed assumptions by virtue of KKMF principle or Fan-Browder fixed point theorem and propose the pseu-solution of minimax inequality. Mild continuity named pseudocontinuity and mild convexity are introduced for the existence results and generalize the present results in the literature. Some other cases of minimax inequality with pseudocontinuity are given in various ways. As applications, we introduce some pseu-Nash equilibrium for n-person noncooperative game and obtain some relaxed existence theorems.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 11401124 and No. 71461003), and the Natural Science Foundation of Guizhou Province (Grant No. QKH[2016]7424,7425). The authors acknowledge these supports.

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Authors and Affiliations

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

    Xiaoling Qiu & Dingtao Peng

Authors
  1. Xiaoling Qiu
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  2. Dingtao Peng
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Corresponding author

Correspondence to Xiaoling Qiu .

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Editors and Affiliations

  1. Fuzhou University, Fuzhou, Fujian, China

    Deng-Feng Li

  2. Chinese Academy of Sciences, Beijing, China

    Xiao-Guang Yang

  3. University of Twente, Enschede, The Netherlands

    Marc Uetz

  4. Northwestern Polytechnical University, Xi'an, China

    Gen-Jiu Xu

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Qiu, X., Peng, D. (2017). Some Relaxed Solutions of Minimax Inequality for Discontinuous Game. In: Li, DF., Yang, XG., Uetz, M., Xu, GJ. (eds) Game Theory and Applications. China GTA China-Dutch GTA 2016 2016. Communications in Computer and Information Science, vol 758. Springer, Singapore. https://doi.org/10.1007/978-981-10-6753-2_7

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  • DOI: https://doi.org/10.1007/978-981-10-6753-2_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6752-5

  • Online ISBN: 978-981-10-6753-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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