Induced Stackelberg Equilibrium Seeking via Iterative Tikhonov Regularization

TL;DR

This paper proposes a novel iterative Tikhonov regularization method for Stackelberg equilibrium seeking that handles multiple followers' equilibria by inducing a unique equilibrium through incentive augmentation.

Contribution

It introduces an optimal equilibrium selection mechanism in Stackelberg games using a vanishing incentive term and a follower-agnostic iterative method.

Findings

The method converges to a unique equilibrium under multiple followers' equilibria.

The leader can steer the followers' game towards a desired equilibrium.

The approach is robust to the presence of multiple Nash equilibria.

Abstract

Existing methods for learning Stackelberg equilibria typically assume that the followers' (variational, generalized) Nash equilibrium is unique. However, in the presence of multiple equilibria, without a selection convention, the problem may become ill-posed, thus leading standard algorithms to potentially fail to converge. This paper addresses this issue by introducing an optimal selection at the lower-level game, hereby defining a Stackelberg game with induced equilibrium selection. To this end, we enable the leader to augment the followers' game with an additional vanishing term that acts as an incentive. We then propose a follower-agnostic zeroth-order method, whereby the leader converges to a solution of the resulting problem by iteratively probing the followers and jointly updating its decision variable and the incentive term.