Stackelberg Population Dynamics: A Predictive-Sensitivity Approach

Hierarchical decision-making processes traditionally modeled as bilevel optimization problems are widespread in modern engineering and social systems. In this work, we deal with a leader population of followers hierarchical order play. general, problem can be leader–follower Stackelberg equilibrium using mathematical program constraints. We propose two interconnected dynamical systems to dynamically solve between follower single time scale by predictive-sensitivity conditioning interconnection. For the leader’s problem, developed gradient descent algorithm based on total derivative, for followers’ used dynamics framework model interacting strategic agents. extended concept differential dynamics. Theoretical guarantees stability proposed learning presented. Finally, distributed energy resource coordination is solved via pricing approach. Some simulation experiments presented illustrate effectiveness framework.