Nash Equilibrium Seeking via Neurodynamic Optimization and Application to Analog Circuits

This paper proposes three gradient-based neurodynamic optimization approaches for Nash equilibrium seeking in non-cooperative games. The decoupled-gradient and coupled-gradient neurodynamic optimization approaches achieve Nash equilibrium with different fixed-time convergence upper bounds, which are invariant to initial conditions, while the proposed mixed-gradient neurodynamic approach exponentially converges to the Nash equilibrium. The robustness of the proposed fixed-time neurodynamic approaches under vanishing disturbances is also investigated. In addition, three novel analog circuit frameworks are introduced, where the actions of neurons are simulated through a feedback loop composed of multipliers, operational amplifiers, resistors, capacitors, and other basic operation models. The circuits demonstrate that the stable output voltages correspond to the Nash equilibrium. Finally, an example is simulated on Multisim 14.3 to validate the superiority and practicality of the proposed analog circuits. © 2025 IEEE.