Fast Nash Equilibrium Seeking in Multi-Group Resource Allocation Networked Game

This paper develops fast algorithms for Nash equilibrium (NE) seeking in multi-group distributed resource allocation games (DRAG) subject to feasibility-preservation and time-critical requirements for real-time implementation. The considered framework captures hybrid cooperative–competitive interactions among agents, where cooperation arises within groups while conflict exists across groups. Two classes of multi-group DRA games, namely the intra-independent distributed resource allocation game (IIDRAG) and the intra-dependent distributed resource allocation game (IDDRAG), are investigated. Two distributed NE seeking algorithms for both cases are proposed. By exploiting a Laplacian-matrix-based affine transformation, the developed algorithms maintain the hard supply–demand balance of each group, which is desirable for real-time implementation that requires feasibility preservation. Moreover, the sampled-data communication mechanism enables specified-time convergence to the NE while reducing communication burden. It is proved that both algorithms achieve convergence to the NE at a prescribed settling time. Numerical examples further illustrate the effectiveness of the specified-time algorithms and hard supply–demand balance preservation.