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Browder type fixed point theorems and Nash equilibria in generalized games

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Abstract

In this paper, we present two generalizations of the well-known Browder fixed point theorem, one of which is equivalent to the well-known Fan–Knaster–Kuratowski–Mazurkiewicz theorem. As applications, we apply these fixed point theorems to derive existence theorems for Nash equilibria in generalized games which generalize some existing existence theorems in the literature, including the well-known equilibrium existence theorem by Arrow and Debreu (Econometrica 22:265–290, 1954) and the existence theorem by Cubiotti (Int J Game Theory 26:267–273, 1997).

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Acknowledgements

The authors would like to thank the referees for their helpful and inspiring suggestions and comments which resulted significant improvements to the paper. We also would like to thank the referee for providing us some most recent references related to our work.

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Authors and Affiliations

  1. China (Xi’an) Institute for Silk Road Research, Xi’an University of Finance and Economics, Xi’an, 710100, Shaanxi, People’s Republic of China

    Jiuqiang Liu & Mingyu Wang

  2. Department of Mathematics, Eastern Michigan University, Ypsilanti, MI, 48197, USA

    Jiuqiang Liu

  3. College of Business, Xi’an University of Finance and Economics, Xi’an, 710100, Shaanxi, People’s Republic of China

    Yi Yuan

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  1. Jiuqiang Liu
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Correspondence to Jiuqiang Liu.

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Liu, J., Wang, M. & Yuan, Y. Browder type fixed point theorems and Nash equilibria in generalized games. J. Fixed Point Theory Appl. 22, 71 (2020). https://doi.org/10.1007/s11784-020-00806-4

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  • DOI: https://doi.org/10.1007/s11784-020-00806-4

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