Lecture 2

Question 1

What are two critiques of the Nash Equilibrium?

Answer 1

1. Non-uniqueness: Haw can there be mulitple equilibrium?
2. Complexity: Very hard to compute and so is it realistic?

Question 2

What is the obedience constraint in a correlated equilibrium?

Answer 2

For the correlation device to be successfull, it must be that every player is better off following the device given all strategies and all beliefs.

Question 3

Give two important facts about correlated equilibriums.

Answer 3

1. If a strategy profile is NE, then it is a correlated equilibrium. (i.e. all NE are Corr. Eq.)
2. Any convex combination of correlated equilibrium payoff profiles are correlated equilibrium payoffs.

Question 4

Why are the greatest and smallest rationalizable action profiles (in supermodular games) correlated equilibria?

Answer 4

Greatest/smallest rationalizable action profiles are NE and all NE are Corr. Eq.

Question 5

Prove the following proposition. (iff)

Answer 5

See lecture bc wayy to long, i doubt he’ll ask for that in class.

Question 6

Prove the following proposition.

Answer 6

Question 7

Prove the following proposition.

Answer 7

Question 8

Answer 8