Dominant strategies are considered as better than other strategies, no matter what other players might do. In game theory, there are two kinds of strategic dominance:
a strictly dominant strategy is a strategy that always provides greater utility to a the player, no matter what the other player’s strategy is.
a weakly dominant strategy is a strategy that provides at least the same utility for all the other player’s strategies, and strictly greater for some strategy.
Elimination of Dominant Stategies
The iterated elimination (or deletion) of dominated strategies (also denominated as IESDS or IDSDS) is one common technique for solving games that involves iteratively removing dominated strategies.
In the first step, at most one dominated strategy is removed from the strategy space of each of the players since no rational player would ever play these strategies.
This results in a new, smaller game. Some strategies—that were not dominated before—may be dominated in the smaller game.
The first step is repeated, creating a new even smaller game, and so on. The process stops when no dominated strategy is found for any player.
A good example of elimination of dominated strategy is the analysis of the Battle of the Bismarck Sea.
In this game, as depicted in the above game matrix, Kenney has no dominant strategy (the sum of the payoffs of the first strategy equals the sum of the second strategy), but the Japanese do have a weakly dominating strategy, which is to go North (the payoffs are equal for one strategy but strictly better for the other).
Since only one of them has a dominant strategy, there is no dominant strategy equilibrium. We must then proceed by eliminating dominated strategies.
As we’ve already mentioned, for the Japanese strategy ‘go North’ weakly dominates strategy ‘go South’.
Therefore, we eliminate the strategy ‘go South’ for the Japanese, who will go North.
Now that we only consider the Japanese going North, Kenney’s strategy ‘go North’ is strictly dominant over strategy ‘go South’, which will be eliminated.
Therefore, North-North is the weak-dominance equilibrium.
