In a two-player game, if both players have a dominant strategy that leads to a Nash equilibrium, what can be concluded about their strategies?

In a two-player game, a dominant strategy for each player means that no matter what the other player does, each player will always choose their dominant strategy because it leads to the best outcome for them. When both players have a dominant strategy, and they choose to play it, this results in a Nash equilibrium, which is a situation where neither player can improve their outcome by changing their strategy alone. This means that both players are making the best decision they can, given the decision of the other player. For example, if Player A always chooses to play "rock" and Player B always chooses to play "scissors," then they reach a stable point where neither player would want to change their choice since doing so would not benefit them. Therefore, we can conclude that both players are following their best strategies, leading to a predictable and stable outcome in the game.