Group Dominant Strategies: (Extended Abstract)

We introduce a new solution concept for complete information games, which we call equilibrium in group dominant strategies. This concept is the strongest of all known solution concepts so far, since it encompasses both the ideas behind the concepts of dominant strategies and strong equilibrium. Because of its strength, a solution in group dominant strategies does not exist in any interesting game; however, as we show, such solutions can be achieved in various rich settings with the use of mediators.