  Multi-defender Stackelberg Security Games (MSSG) have recently gained
increasing attention in the literature. However, the solutions offered to date
are highly sensitive, wherein even small perturbations in the attacker's
utility or slight uncertainties thereof can dramatically change the defenders'
resulting payoffs and alter the equilibrium. In this paper, we introduce a
robust model for MSSGs, which admits solutions that are resistant to small
perturbations or uncertainties in the game's parameters. First, we formally
define the notion of robustness, as well as the robust MSSG model. Then, for
the non-cooperative setting, we prove the existence of a robust approximate
equilibrium in any such game, and provide an efficient construction thereof.
For the cooperative setting, we show that any such game admits a robust
approximate alpha-core, provide an efficient construction thereof, and prove
that stronger types of the core may be empty. Interestingly, the robust
solutions can substantially increase the defenders' utilities over those of the
non-robust ones.
