Whenever both players have a dominant strategy in a Nash game, that strategy will determine the outcome.

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When both players have a dominant strategy, it means that no matter what the other player does, one player's strategy will always give them a better outcome than any other strategy they could choose. In this situation, there is a unique Nash equilibrium where both players play their dominant strategy, and this strategy combination will determine the outcome of the game. When both players have a dominant strategy, it means that regardless of what the other player chooses, one particular strategy will always yield the best outcome for the player with the dominant strategy. In such cases, both players will choose their dominant strategies and those strategies will determine the outcome of the game. This is a key concept in game theory known as the Nash equilibrium.

Whenever Both Players Have a Dominant Strategy in a Nash