Question

Does any pure strategy NE (Nash Equilibrium) involve a weakly dominated strategy?

A) Yes
B) No
C) It depends on the game
D) Only in certain games

Answer 1

In a Nash Equilibrium (NE), no pure strategy involves a weakly dominated strategy.

Step-by-step explanation:

In any game, a weakly dominated strategy is one that is always worse than another strategy, regardless of what the other player does. A strictly dominated strategy is one that is always worse than another strategy, and there is another strategy that is always better, regardless of what the other player does.

In a Nash Equilibrium (NE), each player is playing their best response to the other player's strategy. In order for a pure strategy NE to exist, no player can have a weakly dominated strategy. This is because if a player has a weakly dominated strategy, they would have a better response to their opponent's strategy, which means the current strategy cannot be a NE.

Therefore, the answer to the question is B) No, no pure strategy NE involves a weakly dominated strategy.