Prelim 1

Question 1

What are the characteristics of the prisoner’s dilemma?

Answer 1

2 dominant strategies & 1 Nash equilibrium

Question 2

What are the characteristics of the Fed Game?

Answer 2

1 dominant strategy & 1 Nash equilibrium

Question 3

What are the characteristics of the Sports Game? Describe story

Answer 3

Book used tennis as ex., same as goalies; don’t know which side opponent plays,

Question 4

What are the characteristics of Assurance? Book example

Answer 4

Gimme Coffee vs. Starbucks, ppl don’t know where to go, prefer starbucks, but there’s no strategy; 2 Nash equilibrium, no conflicting payouts

Question 5

What is a symmetric Nash equilibrium?

Answer 5

same payout

Question 6

Elsa game: Find a symmetric Nash equilibrium to this game. That is, what number is a best response to everyone else submitting that same number?

Answer 6

At a symmetric Nash equilibrium, all students will be choosing the same number. From parts (b) and (c) above, we see that there is an incentive to deviate from any number played by everyone else in the class if that number is positive. Zero, however, works as a symmetric Nash equilibrium strategy because it is its own best response: 0 = 0/2.

Question 7

Elsa game: Which strategies are rationalizable in this game?

Answer 7

To find rationalizable strategies to this game, use iterated elimination of never-best responses. We know from part (a) that any number greater than 50 is never a best response. On the basis of this fact, we determine that 50/2 = 25 is also never a best response. You continue this iterated elimination until you are left with the only rationalizable strategy in the game, which is choosing zero

Question 8

Why is (U, LR) not subgame perfect?

Answer 8

(U,LR) is not subgame perfect since player 2 would play L conditional on player 1 having played D. Thus playing LR is an empty-threat on the part of player 2 if player 1 were to actually play D

Question 9

What are the characteristics of Chicken?

Answer 9

2 dominant strategies, 2 Nash equilibria

Question 10

What are the characteristics of Battle of the Sexes?

Answer 10

2 Nash equilibria with “conflicting” payouts; different payouts for different payouts and it’s not 100% clear that with negotiations you can end up satisfactory