Prescribed-Time Nash Equilibrium Seeking for Multicoalition Games With Heterogeneous General Linear Dynamics Over Unbalanced Digraphs

This article investigates the Nash equilibrium (NE) seeking problems for multicoalition games with heterogeneous general linear dynamics over unbalanced digraphs. The coalition can be regarded as a virtual player but the true decision-makers are the actual players themselves which can only access to their own cost functions. To deal with the unbalanced digraphs, the left eigenvector is estimated and its prescribed-time convergence is illuminated with the time transfer approach. Then the NE seeking part and the output regulation part are designed to adapt the dynamics of the players. The initial values of the auxiliary vectors are selected to avoid utilizing the out-degree information. The steady state of the closed-loop system is analyzed and the prescribed-time convergence is proved based on the Lyapunov method. Finally, the simulation results of both the mobile sensor connectivity game and the electricity market game are presented to show the effectiveness of the proposed algorithm.