Algorithm and application of the Stackelberg game

Abstract

The multi-agent decision-making problem (MADP) finds an equilibrium among decision-makers who interact with each other to achieve their own goals. This problem is modeled as either a Nash game or a Stackelberg game, depending on whether the relationships among decision-makers are horizontal or hierarchical. In this paper, we address theoretical and applied research on finding the equilibrium of MADPs from a game-theoretic perspective. First, we propose a method for managing a shared energy storage system (ESS) based on capacity trading, model it as a generalized Nash game, and empirically verify that the proposed method is more effective than individual ESS management. Second, we define the equilibrium of a Stackelberg game and propose an algorithm to compute the equilibrium based on the gradient descent algorithm. Next, we propose a method for managing a shared ESS based on incentive design, model it as a Stackelberg game, and empirically validate that the proposed method is more efficient than traditional shared ESS management. Finally, we propose a meta-learning approach that considers task relationships and interpret it from a game-theoretic perspective to introduce a novel gradient-based meta-learning algorithm.