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The concept of leader--follower (or Stackelberg) equilibrium plays a centralrole in a number of real--world applications of game theory. While the casewith a single follower has been thoroughly investigated, results with multiplefollowers are only sporadic and the problem of designing and evaluatingcomputationally tractable equilibrium-finding algorithms is still largely open.In this work, we focus on the fundamental case where multiple followers play aNash equilibrium once the leader has committed to a strategy---as weillustrate, the corresponding equilibrium finding problem can be easily shownto be $\mathcal{FNP}$--hard and not in Poly--$\mathcal{APX}$ unless$\mathcal{P} = \mathcal{NP}$ and therefore it is one among the hardest problemsto solve and approximate. We propose nonconvex mathematical programmingformulations and global optimization methods to find both exact and approximateequilibria, as well as a heuristic black box algorithm. All the methods andformulations that we introduce are thoroughly evaluated computationally.

Methods for finding leader--follower equilibria with multiple followers