Multi-Leader Congestion Games with an Adversary

We study a multi-leader single-follower congestion game where multiple users (leaders) choose one resource out of set resources and, after observing the realized loads, an adversary (single-follower) attacks with maximum loads causing additional costs for leaders. For resulting strategic among leaders, we show that pure Nash equilibria fail to exist and therefore, consider approximate instead. As our first main result, existence K-approximate equilibrium can always be guaranteed, K (approximately equal 1.1974) is unique solution cubic polynomial equation. To this end, give time combinatorial algorithm which computes equilibrium. The factor tight, meaning there instance does not admit A-approximate any A < K. Thus = smallest possible value such guaranteed considered game. Secondly, focus on given fixed instance. how compute efficiently best equilibrium, is, all