On the Equilibrium of a Class of Leader-Follower Games with Decision-Dependent Chance Constraints

TL;DR

This paper investigates the existence of equilibrium in a leader-follower game with decision-dependent chance constraints, transforming the problem into a tractable form and proving equilibrium existence using fixed-point theory.

Contribution

It introduces a novel approach to handle decision-dependent uncertainties in leader-follower games by transforming chance constraints into second-order cone constraints and establishing equilibrium existence.

Findings

Existence of at least one equilibrium point proven.

Transformation of chance constraints simplifies the game model.

Numerical example illustrates the impact of decision-dependent uncertainties.

Abstract

In this paper, we study the existence of equilibrium in a single-leader-multiple-follower game with decision-dependent chance constraints (DDCCs), where decision-dependent uncertainties (DDUs) exist in the constraints of followers. DDUs refer to the uncertainties impacted by the leader's strategy, while the leader cannot capture their exact probability distributions. To address such problems, we first use decision-dependent ambiguity sets under moment information and Cantelli's inequality to transform DDCCs into second-order cone constraints. This simplifies the game model by eliminating the probability distributions. We further prove that there exists at least one equilibrium point for this game by applying Kakutani's fixed-point theorem. Finally, a numerical example is provided to show the impact of DDUs on the equilibrium of such game models.