If all players in a game have a dominant strategy, then there can only be one pure strategy Nash equilibrium to the game.

Question

Quizplus · Accepted Answer

If all players have a dominant strategy, then they will all choose that strategy regardless of what the other player(s) chooses. This means that there is only one possible outcome, which is the one that results from all players choosing their dominant strategy. Therefore, there can only be one pure strategy Nash equilibrium in this scenario.

If All Players in a Game Have a Dominant Strategy