The relationship between a pure-strategy Nash equilibrium and a dominant-strategy equilibrium is that:
A) a dominant-strategy equilibrium is a special case of a pure-strategy Nash equilibrium.
B) a pure-strategy Nash equilibrium is a special case of a dominant-strategy equilibrium.
C) they are the same.
D) there may not be a dominant-strategy equilibrium, but there always is a pure-strategy Nash equilibrium.
E) they are mutually exclusive and exhaustive, in that a dominant-strategy equilibrium is the same thing as a mixed-strategy Nash equilibrium.

Question

Quizplus · Accepted Answer

A dominant-strategy equilibrium is a situation in which each player's optimal strategy is independent of the strategies chosen by other players. A pure-strategy Nash equilibrium is a situation in which each player's strategy is a best response to the strategies chosen by the other players. Therefore, a dominant-strategy equilibrium is a special case of a pure-strategy Nash equilibrium, where each player's dominant strategy happens to be their best response to the other players. However, not all pure-strategy Nash equilibria are dominant-strategy equilibria, since there may be cases where a player has multiple best responses, but only one dominant strategy.

The Relationship Between a Pure-Strategy Nash Equilibrium and a Dominant-Strategy