Distributed Generalized Nash Equilibrium Seeking for Constrained Population Games via Consensus-Based Revision Protocols

This study addresses distributed decision-making in multi-agent systems under shared constraints. Existing methods often fail to guarantee strict constraint satisfaction or require sensitive parameter tuning. We propose a novel algorithm that integrates a revision protocol with a consensus mechanism. The key innovation is a built-in, parameter-free constraint-checking function within the revision protocol, which automatically halts infeasible strategy updates. This approach enables agents using only local neighbor communication to seek a Generalized Nash Equilibrium (GNE). Theoretical analysis proves that the algorithm converges exponentially. Extensive simulations demonstrate its superiority: it achieves faster convergence and ensures strict per-iteration constraint satisfaction, significantly outperforming traditional gradient descent and penalty-based methods across various network topologies.