Variational Inequality Formulation of a Class of Multi‐Leader‐Follower Games

The multi‐leader‐follower game can be looked on as a generalization of the Nash equilibrium problem and the Stackelberg game, which contains several leaders and a number of followers. Recently, the multi‐leader‐follower game has been drawing more and more attention, for example, in electricity power markets. However, when we formulate a general multi‐leader‐follower game as a single‐level game, it will give rise to a lot of problems, such as the lack of convexity and the failure of constraint qualifications. In this paper, to get rid of these difficulties, we focus on a class of multi‐leader‐follower games that satisfy some particular, but still reasonable assumptions, and show that these games can be formulated as ordinary Nash equilibrium problems, and then as variational inequalities. We establish some results on the existence and uniqueness of a leader‐follower Nash equilibrium. We also present illustrative numerical examples from an electricity power market model.