We propose a two-layer, semidecentralized 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 the 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.

Local Stackelberg Equilibrium Seeking in Generalized Aggregative Games

Fabiani, Filippo;
2022-01-01

Abstract

We propose a two-layer, semidecentralized 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 the 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.
2022
Game theory, hierarchical systems, optimization, Stackelberg equilibrium
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/25784
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