Prescribed-Time Distributed Generalized Nash Equilibrium Seeking

TL;DR

This paper introduces a fully distributed algorithm that guarantees convergence to a generalized Nash equilibrium within a user-prescribed finite time, using a novel combination of observer, optimization, and consensus dynamics.

Contribution

It develops the first fully distributed prescribed-time GNE seeking algorithm with a centralized convergence foundation and a novel gain synchronization technique.

Findings

Algorithm guarantees convergence at the prescribed time T.

Simulation results validate effectiveness on Nash-Cournot and sensor coverage problems.

The approach is projection-free and ensures constraint satisfaction at T.

Abstract

This paper proposes the first fully distributed algorithm for finding the Generalized Nash Equilibrium (GNE) of a non-cooperative game with shared coupling constraints and general cost coupling at a user-prescribed finite time T. As a foundation, a centralized gradient-based prescribed-time convergence result is established for the GNE problem, extending the optimization Lyapunov function framework to gradient dynamics, the only known realization among existing alternatives that naturally decomposes into per-agent computations. Building on this, a fully distributed architecture is designed in which each agent concurrently runs three coupled dynamics: a prescribed-time distributed state observer, a gradient-based optimization law, and a dual consensus mechanism that enforces the shared-multiplier requirement of the variational GNE, thus guaranteeing convergence to the same solution as the centralized case. The simultaneous operation of these layers creates bidirectional perturbations between consensus and optimization, which are resolved through gain synchronization that matches the temporal singularities of the optimization and consensus layers, ensuring all error components vanish exactly at T. The Fischer-Burmeister reformulation renders the algorithm projection-free and guarantees constraint satisfaction at the deadline. Numerical simulations on a Nash-Cournot game and a time-critical sensor coverage problem validate the approach.