Every dominant strategy equilibrium is a Nash equilibrium, but not every Nash equilibrium is a dominant strategy equilibrium.

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Quizplus · Accepted Answer

This statement is true. A dominant strategy equilibrium is a type of Nash equilibrium where each player's dominant strategy is to choose a specific action regardless of what the other player does. Every dominant strategy equilibrium is also a Nash equilibrium, because each player is playing their best response given the other player's action. However, not every Nash equilibrium is a dominant strategy equilibrium, because in a Nash equilibrium, each player may not have a dominant strategy and may be choosing the best response to the other player's action.

Every Dominant Strategy Equilibrium Is a Nash Equilibrium, but Not