Dominance and Nash Equilibria

Definition

Strategy s is strictly dominant if strategy s strictly dominates every other possible strategy.

Strategy s is weakly dominant if strategy s dominates all other strategies, but some are only weakly dominated.

Strategy s is strictly dominated if some other strategy exists that strictly dominates s.

Strategy s is weakly dominated if some other strategy exists that weakly dominates s.


Important!

1. A strictly dominant strategy must be played in Nash Equilibria.

2. Strictly dominated strategies cannot be played in Nash Equilibria.

3. Weakly dominated strategies may be played in Nash Equilibria.

4. If, after completing iterated elimination of strongly dominated strategies, there is only one strategy for each player remaining, that strategy set is the unique Nash equilibrium.

5. If, after completing iterated elimination of weakly dominated strategies, there is only one strategy for each player remaining, that strategy set is also a Nash equilibrium. (The Nash equilibrium found by eliminating weakly dominated strategies may not be the only Nash equilibrium.)

 http://en.wikipedia.org/wiki/Strategic_dominance