Dominant-Strategy Equilibrium vs Nash Equilibrium

Question

What's the difference between dominant-strategy solution and Nash Equilibrium? I could not tell the difference judging from the definitions. It would be appreciated if these concepts can be illustrated in a simple game (other than prisoner's dilemma as in that case both solutions will be the same .. and I cannot tell the difference).

Answer 1

A (pure strategy) nash equilibrium can still involve strategies that are weakly dominated. However, a nash equilibrium cannot involve a strategy that is strictly dominated by another.

On the other hand, a dominant strategy equilibrium is when all players play a strictly dominant strategy. A nash equilibrium does not imply that both players always play a strictly dominant strategy.