Week 8 - Cooperation in repeated games

Question 1

Why might people ‘cooperate’ in a one shot prisoners dilemma

Answer 1

1. mistake/misunderstanding the game
2. inequality aversion, altruism

Question 2

When you add social preferences such as inequality aversion, what happens to the game table and therefore equilibrium?

Answer 2

You change the game table to represent utilities instead of monetary payoffs. You use the utility function to calculate the new numbers. Equilibrium can change

Question 3

What are 2 interpretations of infinitely repeated games?

Answer 3

1. Uncertain future - the game continues with probability x and therefore payoffs in the later period are discounted
2. impatience - The game is infinitely repeated but the players are impatient, valuing earlier payoffs more than later ones

Question 4

What are 3 repeated game strategies?

Answer 4

1. grim trigger
2. tit for tat
3. tit for 2 tats

Question 5

What is the equation for payoffs in an infinitely repeated prisoners dilemma?

Answer 5

pi1 +dpi2 + (1-d)0 + d^2 pi3 + d(1-d)0…

Question 6

What is the payoff is players pay TFT in every round?

Answer 6

pi1/1-d

Question 7

In a TFT repeated game, how do you work out the incentive to deviate once?

Answer 7

Workout payoffs from both strategies
See the difference in payoffs (usually delta would be in one)
Say there are incentives to deviate if x>=y.
Solve for delta i.e. the continuation probability

Question 8

What are the rollback equilibrium strategies in a repeated prisoners dilemma?

Answer 8

TFT
D forever
grim trigger
- It depends on the strategy of the other player to decide which strategy is the best

Question 9

In a prisoners dilemma, what is the difference between an infinite and a finite repeated game as we approach the end?

Answer 9

In a finite game, as we approach the end less and less people cooperate.

Question 10

If we play a prisoners dilemma sequentially, what will happen?

Answer 10

Nothing. People still play the dominant strategy of defect

Question 11

What are contingent strategies?

Answer 11

A move you are going to do depends on the previous moves

Question 12

What is the formula for finding an infinite sum of a fixed payoff in repeated games?

Answer 12

5/1-delta

delta = probability game will continue until the next round