Stability of equilibria for population games with uncertain parameters under bounded rationality

Under the assumption that the range of varying uncertain parameters is known, some results of existence and stability of equilibria for population games with uncertain parameters are investigated in this paper. On the basis of NS equilibria in classical noncooperative games, the concept of NS equili...

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Bibliographic Details
Published in:Journal of inequalities and applications 2021-01, Vol.2021 (1), p.1-13, Article 15
Main Authors: Zhao, Wei, Yang, Hui, Deng, Xicai, Zhong, Chongyi
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Bounded rationality
Convexity
Existence
Fixed points (mathematics)
Game theory
Games
Mathematical models
Mathematics
Mathematics and Statistics
NS equilibrium
Parameter uncertainty
Population
Population games
Stability
Uncertain parameters
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Summary:Under the assumption that the range of varying uncertain parameters is known, some results of existence and stability of equilibria for population games with uncertain parameters are investigated in this paper. On the basis of NS equilibria in classical noncooperative games, the concept of NS equilibria for population games with uncertain parameters is defined. Using some hypotheses about the continuity and convexity of payoff functions, the existence of NS equilibria in population games is also proved by Fan–Glicksberg fixed point theorem. Furthermore, we establish a bounded rationality model of population games with uncertain parameters, and draw the conclusions about the stability of NS equilibrium in this model by constructing the rationality function and studying its properties.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02544-0