Strategic dominance

In game theory, a strategy A dominates another strategy B if A will always produce a better result than B, regardless of how any other player plays. Some very simple games (called straightforward games) can be solved using dominance.

A strategy that is not dominated by another strategy is called admissible. A common assumption in game theory is that rational players use admissible strategies.

Terminology

A player can compare two strategies, A and B, to determine which one is better. The result of the comparison is one of:

B strictly dominates (>) A: choosing B always gives a better outcome than choosing A, no matter what the other players do.

B weakly dominates (≥) A: choosing B always gives at least as good an outcome as choosing A, no matter what the other players do, and there is at least one set of opponents' actions for which B gives a better outcome than A. (Notice that if B strictly dominates A, then B weakly dominates A. Therefore, we can say "B dominates A" to mean "B weakly dominates A".)

B is weakly dominated by A: there is at least one set of opponents' actions for which B gives a worse outcome than A, while all other sets of opponents' actions give B the same payoff as A. (Strategy A weakly dominates B).

B is strictly dominated by A: choosing B always gives a worse outcome than choosing A, no matter what the other player(s) do. (Strategy A strictly dominates B).

Neither A nor B dominates the other: B and A are not equivalent, and B neither dominates, nor is dominated by, A. Choosing A is better in some cases, while choosing B is better in other cases, depending on exactly how the opponent chooses to play.