The Generic Uniqueness and Well-Posedness of Nash Equilibria for Stable Population Games

doi:10.1007/s40305-019-00281-w

Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (2): 455-464.doi: 10.1007/s40305-019-00281-w

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The Generic Uniqueness and Well-Posedness of Nash Equilibria for Stable Population Games

Wen-Sheng Jia^1,2, Xiao-Ling Qiu^1,2, Ding-Tao Peng^1,2

1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China;
2. Key Laboratory of Games Decision Making and Control Systems, Guiyang 550025, China

Received:2018-10-30 Revised:2019-04-03 Online:2021-06-30 Published:2021-06-08
Contact: Xiao-Ling Qiu, Wen-Sheng Jia, Ding-Tao Peng E-mail:xlqiu@gzu.edu.cn;wsjia@gzu.edu.cn;dtpeng@gzu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (No.11561013),the Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China (No.[2015]192),the Joint Foundation of Guizhou Province and Guizhou University (Nos.QKH[2014]7643,QKH[2016]7425) and the Introduced Talent Foundation of Guizhou University (Nos.[2014]05,[2018]11).

Abstract

Abstract: This paper aims at studying a new kind of stable population games introduced by J. Hofbauer and H. Sandholm in 2009. We first construct a complete distance space M consisting of stable population games and show that most of stable population games have unique Nash equilibrium point that according to Baire’s category theorem. It implies that every stable population game that possesses more than one Nash equilibrium can be approached arbitrarily by a sequence of the stable population game each of which has a unique Nash equilibrium. Then, we construct a bounded rationality function and deduce some results on the generic well-posedness implying Tikhonov well-posedness and Hadamard well-posedness for stable population games.

Key words: Stable population games, Generic uniqueness, Generic well-posedness, Bounded rationality

CLC Number:

Wen-Sheng Jia, Xiao-Ling Qiu, Ding-Tao Peng. The Generic Uniqueness and Well-Posedness of Nash Equilibria for Stable Population Games[J]. Journal of the Operations Research Society of China, 2021, 9(2): 455-464.

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The Generic Uniqueness and Well-Posedness of Nash Equilibria for Stable Population Games

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