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The HoneyComb Paradigm for Research on Collective Human Behavior
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Prescribed-Time Nash Equilibrium Seeking for Multicoalition Games With Heterogeneous General Linear Dynamics Over

Yiyang Chen, Xiaoduo Li, Zhi Feng

    IEEE Transactions on Cybernetics
    |September 16, 2025
    PubMed
    Summary

    This study addresses Nash equilibrium (NE) seeking in multicoalition games with complex dynamics on unbalanced networks. A novel algorithm ensures players reach equilibrium efficiently, demonstrated through simulations in connectivity and market games.

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    Area of Science:

    • Control Theory
    • Game Theory
    • Networked Systems

    Background:

    • Multicoalition games present challenges in achieving Nash equilibrium (NE) due to complex player interactions and network structures.
    • Heterogeneous linear dynamics and unbalanced digraphs in these games complicate traditional equilibrium-seeking methods.

    Purpose of the Study:

    • To develop and analyze an algorithm for seeking Nash equilibrium in multicoalition games with heterogeneous general linear dynamics over unbalanced digraphs.
    • To address the specific challenges posed by unbalanced network topologies in distributed decision-making scenarios.

    Main Methods:

    • Estimation of the left eigenvector using a time transfer approach to handle unbalanced digraphs.
    • Design of adaptive control strategies for both Nash equilibrium seeking and output regulation.
    • Utilization of Lyapunov stability theory to prove prescribed-time convergence of the closed-loop system.

    Main Results:

    • The proposed algorithm effectively achieves Nash equilibrium seeking in the presence of unbalanced network structures.
    • Prescribed-time convergence of the system dynamics is rigorously proven.
    • Simulations demonstrate the algorithm's efficacy in a mobile sensor connectivity game and an electricity market game.

    Conclusions:

    • The developed method provides a robust solution for Nash equilibrium seeking in complex multicoalition games.
    • The approach is effective for systems with heterogeneous dynamics and unbalanced communication topologies.
    • The findings have practical implications for distributed optimization and control in networked systems.