Distributed Nash Equilibrium Seeking in Two-Coalition Zero-Sum Games Under Edge Agreements

This paper investigates the Nash equilibrium seeking problem in two coalitions of agents constrained by edge agreements, where all agents within the same coalition are collectively cooperative to minimize the sum of their individual costs. The edge agreements are linear constraints imposed by adjacent agents, which integrate several coordination control objects (e.g., consensus control, cluster consensus control and formation control) into a unified framework. We first propose a distributed algorithm based on the Rosen's gradient projection method and subgradient for Nash equilibrium seeking. Then, it is strictly proved that the proposed algorithm can solve the distributed Nash equilibrium seeking problem under edge agreements. Finally, a simulation example is provided to validate the effectiveness of the algorithm.