True of False 1. In a Nash Equilibrium, a player never play a strictly dominated

Question

True of False

1. In a Nash Equilibrium, a player never play a strictly dominated strategy.

2. In a Nash Equilibrium, everyone must be playing a strategy that is either strictly dominated or weakly dominant.

3. A two-player game in which each player has access to only two possible pure strategies will have at most one Nash equilibrium

4. A two-player game in which each player has access to only two possible pure strategies will have at least one mixed Nash equilibrium.

5. A game has two player and each has two strategies. The strategies are Be Nice and Be Mean. If both players play Be Nice, both get a payoff of 5. If both players play Be Mean, both get payoff of -3. If one player plays Be Nice and the other plays Be Mean, the player who played Be Nice gets 0 and the player who played Be Mean gets 10. Playing Be Mean is a weakly dominant strategy for both players.

Explanation / Answer

1.T A Nash equilibrium is when all players are doing as well as they can given what the other players are doing. If you are playing a strictly dominated strategy you can always do better by shifting to another. 2. F A Nash equilibrium can occur with a strictly dominant strategy as well as a weakly dominant one. 3.F 4. T 5.F If you know the other player is going to be mean, you are better off by playing nice.

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