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Which of the following conditions are necessary for the existence of a Nash equilibrium in a...

Which of the following conditions are necessary for the existence of a Nash equilibrium in a two-player game?

None of the statements associated with this question are correct
The existence of dominant strategies for both players
The existence of a dominant strategy for at least one player
Ability to achieve the highest combined payoff for the two players
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Answer #1

None of the statement is correct. Dominant strategy does play a significant role in determining the Nash equilibrium but it is not a requirement. Nash equilibrium represents a set of strategies that are the best responses of players given the possible strategies of the rivals. In prisoner dilemma case for example the combined payoff is greater under coordinated strategy but selected outcome has a lower combined payoff. Therefore Nash equilibrium can exist without a dominant strategy and without a highest combined payoff achieved.

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