Pessimistic Leader-Follower Equilibria with Multiple Followers

Stefano Coniglio, Nicola Gatti, Alberto Marchesi
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
The problem of computing the strategy to commit to has been widely investigated in the scientific literature for the case where a single-follower is present. In the multi-follower setting though, results are only sporadic. In this paper, we address the multi-follower case for normal-form games, assuming that, after observing the leader's commitment, the followers play pure strategies and reach a Nash equilibrium. We focus on the pessimistic case where, among many equilibria, one minimizing the
more » ... eader's utility is chosen (the opposite case is computationally trivial). We show that the problem is NP-hard even with only two followers, and propose an exact exponential-time algorithm which, for any number of followers, either finds an equilibrium when the game admits a finite one or, if not, an α-approximation of the supremum of the leader' utility, for any α > 0.
doi:10.24963/ijcai.2017/25 dblp:conf/ijcai/Coniglio0M17 fatcat:bvpx7cl4lrcfhmh2atxskj6zw4