The multi-leader-follower game (MLFG) is a generalization of the Stackelberg game which considers bilevel games with a single leader. Here, the individuals (players) are divided into two groups, namely leaders and followers, according to their position (role) in the game. Mathematically, this yields a hierarchical Nash game, where further minimization problems appear in the leaders' optimization problems as constraints. A Nash equilibrium is then given by a multistrategy vector of all players, where no player has the incentive to change his chosen strategy unilaterally.We derive a Nash equilibrium for a quadratic multi-leader-follower game using the nonsmooth best response function of the follower. The existence and uniqueness of solutions are proven for an example and its Nash equilibrium is explicitly computed.
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