Hierarchical Noncooperative Dynamical Systems Under Intra-group and Inter-group Incentives

A framework for hierarchical noncooperative systems with dynamic agents is proposed. In the characterized framework, agents in each group are incentivized by a corresponding group manager who represents the benefits of group utility via an intra-group incentive mechanism. The coefficients in intra-group incentive functions are characterized as the group manager's strategy in this paper. The update rules that can be adopted by the group managers are proposed based on the local state and the payoff information with continual and intermittent observation on the state of the agents from the other groups. Sufficient conditions under which the trajectory of agents' state converges towards the group Nash equilibrium are derived for the proposed update rules. Furthermore, to improve the social welfare of the entire system, we propose an inter-group incentive scheme in the group managers level for a system governor to bring agents' state to a target equilibrium. To deal with the uncertain information on agents' personal payoff functions for the system governor, we present sufficient conditions to guarantee the convergence of agents' state to the target equilibrium. Three numerical examples are provided to illustrate the efficacy of our approach.