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If only one player has a dominant strategy in a game with two players, will there...

If only one player has a dominant strategy in a game with two players, will there be a Nash equilibrium?

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Answer #1

A strategy is said to be dominant if, the pay off the strategy is largest among the available strategy to this players regardless of strategy chosen by other players. Hence, it can be said that a strategy is dominant if it is always superior, compare to any other strategy, for any profile of other player’s action

Since the Nash equilibrium occurs when every player wants to choose the best possible strategy, given the strategies of another player. Once the Nash equilibrium is reached, there is no incentive to change the strategy by the both players.

Hence it can be said that If only one player has a dominant strategy in a game with two players, there will not be a Nash equilibrium.

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