Evaluate whether the statement is true or false. Explain why. a. Dominant strategy equilibrium is a...

Evaluate whether the statement is true or false. Explain why.

a. Dominant strategy equilibrium is a Nash equilibrium.

b. A Nash equilibrium is Pareto efficient.

c. Every subgame perfect Nash equilibrium is a Nash equilibrium.

Solutions

Expert Solution

Solution:

a) Dominant strategy is the one which a player plays, no matter what stratrgy the other player plays. Since, this strategy generates highest payoff than other strategies for a player, it is dominant as it is always chosen others. A dominant strategy equilibrium occurs where all players are playing their dominant strategy. Nash equilibrium is the one where a player is choosing the best response (the one generating highest payoff), given other players best responses. In this sense, since dominant strategy is the best response always, a dominant strategy equilibrium is a Nash equilibrium.

Thus, the given statement is TRUE.

b) A Nash equilibrium is simply the mutual best response of all players. Note that the best response to other players' best response might not always give an efficient solution. Pareto efficient point is the one under which a player cannot do better off without making someone worse-off (that is all players getting a higher payoff simultaneously). However, this is not always the case with the Nash equilibrium. An example for such a case is prisoners' dilemma, under which both players can do better by cooperating, however under equilibrium, both choose to defect.

Thus, the given statement is FALSE.

c) Every subgame perfect Nash equilibrium is the ultimate equilibrium reached when game is being played sequentially. Since, Nash equilibrium itself is a mutual best response of all players in the game, subgame perfect NE is one of them. Basically, a game having a unique SPNE may have more than one NE, and that SPNE is subset of NE.

Thus, the given statement is TRUE.

Rahul Sunny answered 9 months ago

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