L14

Question 1

Define, formally, a Nash Equilibrium?

Answer 1

A Nash equilibrium recommends a strategy to each player that the player cannot improve upon unilaterally, that is, given that the other players follow the recommendation. In other words, if each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. Since the other players are also rational, it is reasonable for each player to expect his opponents to follow the recommendation as well.

Question 2

Why is a solution that isn’t a NE not a credible solution?

Answer 2

Since at least one player will have incentive to change their choice

Question 3

How do we know that if EofD’edS -> unique strategy profile, that this is a NE?

Answer 3

Because a dominated strategy can never be part of an equilibrium since there would then be an incentive for a player to switch actions

Question 4

See and understand

Answer 4

Best response correspondence

Question 5

What are mixed strategies?

Answer 5

When players randomly select from pure strategies with certain probailities