Local Stackelberg equilibrium seeking in generalized aggregative games

TL;DR

This paper introduces a semi-decentralized algorithm for finding local Stackelberg equilibria in aggregative games with coupling constraints, demonstrated through a PEV charging coordination case study.

Contribution

It develops a novel iterative convexification approach for solving the Stackelberg equilibrium problem in aggregative games with coupling constraints.

Findings

Algorithm converges to a local Stackelberg equilibrium.

Effective in hierarchical PEV charging coordination.

Demonstrates practical applicability through numerical case study.

Abstract

We propose a two-layer, semi-decentralized algorithm to compute a local solution to the Stackelberg equilibrium problem in aggregative games with coupling constraints. Specifically, we focus on a single-leader, multiple-follower problem, and after equivalently recasting the Stackelberg game as a mathematical program with complementarity constraints (MPCC), we iteratively convexify a regularized version of the MPCC as inner problem, whose solution generates a sequence of feasible descent directions for the original MPCC. Thus, by pursuing a descent direction at every outer iteration, we establish convergence to a local Stackelberg equilibrium. Finally, the proposed algorithm is tested on a numerical case study involving a hierarchical instance of the charging coordination of Plug-in Electric Vehicles (PEVs).