Local Stackelberg equilibrium seeking in generalized aggregative games

Journal article (2022)

Authors

Filippo Fabiani University of Oxford
Mohammad Amin Tajeddini University of Tehran
Hamed Kebriaei University of Tehran
S. Grammatico Team Bart De Schutter - Mechanical, Maritime and Materials Engineering , Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering
Research Group
Team Sergio Grammatico (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2022 Filippo Fabiani, Mohammad Amin Tajeddini, Hamed Kebriaei, S. Grammatico
DOI: https://doi.org/10.1109/TAC.2021.3077874
Optimization Game theory Cost function Games Convergence Approximation algorithms Wireless networks Standards Couplings Hierarchical systems Stackelberg equilibrium
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Published Date

2022

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Sergio Grammatico

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, a hierarchical instance of the charging coordination problem of Plug-in Electric Vehicles (PEVs).