A fast optimization approach for seeking Nash equilibrium based on Nikaido–Isoda function, state transition algorithm and Gauss–Seidel technique

This paper proposes a fast optimization approach for non-cooperative games with complicated payoff functions (non-smooth, non-concave, etc.). The Nikaido–Isoda function is employed to convert knotty Nash equilibrium problems (NEPs) into large-scale optimization problems with complex objective functi...

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Bibliographic Details
Published in:	Neurocomputing (Amsterdam) Vol. 616; p. 128922
Main Authors:	Zhou, Xiaojun, Wang, Zheng, Huang, Tingwen
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.02.2025
Subjects:	Gauss–Seidel technique Nash equilibrium Non-cooperative game State transition algorithm Gauss–Seidel technique Non-cooperative game Nash equilibrium State transition algorithm
ISSN:	0925-2312
Online Access:	Get full text
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Summary:	This paper proposes a fast optimization approach for non-cooperative games with complicated payoff functions (non-smooth, non-concave, etc.). The Nikaido–Isoda function is employed to convert knotty Nash equilibrium problems (NEPs) into large-scale optimization problems with complex objective functions. To efficiently seek Nash equilibrium, the resulting optimization problems are decomposed into many subproblems where each player tries to maximize its payoff when observing others’ current strategies. All players’ strategies are updated iteratively until reaching Nash equilibrium. Specifically, a dynamic state transition algorithm (STA) is proposed to seek global optima of subproblems at each iteration, and the sequential quadratic programming (SQP) is embedded into dynamic STA for convergence acceleration. A Gauss–Seidel technique is utilized for players’ strategy updates to improve computational efficiency further. Numerical examples drawn from multidisciplinary contexts validate that the proposed approach could effectively seek out Nash equilibrium for simultaneously decreasing the time-consuming remarkably.
ISSN:	0925-2312
DOI:	10.1016/j.neucom.2024.128922