A Timestamp-Based Inertial Best-Response Dynamics for Distributed Nash Equilibrium Seeking in Weakly Acyclic Games

Tan, Shaolin; Fang, Zhihong; Wang, Yaonan; Lü, Jinhu

doi:10.1109/tnnls.2022.3183250

Cited by 4 publications

(1 citation statement)

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“…This recurring theme finds resonance in real-world scenarios, adroitly addressed by Bayesian game (BG), particularly through the Aumann [22] and Harsanyi [23] models, designed to tackle incomplete information challenges. Papers [24][25][26] explore distributed Nash equilibrium seeking strategy in incomplete information scenarios where all the players participate in a common game, and each player can only get the action of their neighbors' rather than all the others. Wu et al proposed a transformation that converts an incomplete information game (Bayesian game) into a full information game [27].…”

Section: Introductionmentioning

confidence: 99%

Modeling and optimization of networked evolutionary game based on incomplete information with switched topologies

Gui,

Gao,

2024

IET Control Theory & Appl

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In the realm of evolutionary game theory, the majority of scenarios involve players with incomplete knowledge, specially regarding their opponents' actions and payoffs compounded by the ever‐shifting landscape of players' interactions. These dynamics present formidable challenges in both the analysis and optimization of game evolution. To address this, a novel model named the networked evolutionary game (NEG) is proposed based on incomplete information with switched topologies. This model captures situations where players possess limited insight into their opponents' benefits, yet make decisions based on their own payoffs while adapting to different networks and new players. To bridge the gap between incomplete and complete information games, R. Selten's transformation method is leveraged, a renowned approach that converts an incomplete information game into an interim agent game, thereby establishing the equivalence of pure Nash equilibria (NE) in both scenarios. Employing the semi‐tensor product (STP) of matrices, a powerful tool in logistic system, the evolution of the model is articulated through algebraic relationships. This enables to unravel the patterns of game evolution and identify the corresponding pure Nash equilibria. By introducing control players, strategically positioned within the game, optimized control is facilitated over the evolutionary trajectory, ultimately leading to convergence towards an optimal outcome. Finally, these concepts are illustrated with a practical example within the paper.

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