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Distributed Generalized Nash Equilibrium Seeking for Monotone Generalized Noncooperative Games by a Regularized
IEEE Transactions on Cybernetics
|August 16, 2021
Summary
This study introduces a new dynamical system and distributed algorithm to find generalized Nash equilibrium (GNE) in complex noncooperative games with constraints. Both methods are proven to converge to the least-norm variational equilibrium, demonstrating effectiveness in numerical examples.
Area of Science:
- Game Theory
- Optimization
- Dynamical Systems
Background:
- Generalized Nash equilibrium (GNE) problems are crucial in noncooperative games.
- Existing methods struggle with set constraints and shared affine inequality constraints.
Purpose of the Study:
- To develop a novel dynamical system for solving GNE problems with set and shared affine inequality constraints.
- To propose a distributed algorithm for GNE seeking using leader-following consensus.
Main Methods:
- A projected gradient-based regularized penalized dynamical system utilizing differentiable penalty functions and time-varying regularization.
- A distributed algorithm leveraging leader-following consensus for players with local information.
Main Results:
- The proposed dynamical system effectively handles inequality and set constraints.
- The distributed algorithm enables GNE seeking with only neighboring information.
- Asymptotic convergence to the least-norm variational equilibrium is proven for both approaches.
Conclusions:
- The novel dynamical system and distributed algorithm offer efficient solutions for complex GNE problems.
- The methods demonstrate robustness and effectiveness through numerical validation.
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