Week 2 - Sequential games

Question 1

What is the benefit of moving first and what type of games see first-mover advantage

Answer 1

Ability to commit to preferred option. Seen in games in which players want to co-ordinate but disagree on what to co-ordinate on

Question 2

What is the benefit of moving 2nd and what type of games see second-mover advantage

Answer 2

The flexibility to adapt to the choices of other players. Seen in sequential zero-sum games e.g. rock-paper-scissors, public auctions

Question 3

What happens when there are indifferences at a node?

Answer 3

There are multiple equilibria

Question 4

What is the ultimatum game?

Answer 4

Player 1 decides how to divide x between them and player 2. Player 2 can either accept or reject. If they reject, both players earn nothing

Question 5

What is the rollback equilibrium in a basic ultimatum game?

Answer 5

The responder will accept anything.

Question 6

Why might the proposer in the ultimatum game send positive amounts? (5)

Answer 6

1. Altruism
2. Inequality aversion
3. Risk aversion - safe to send larger amounts
4. Belief that responder is inequality averse
5. Expecting negative reciprocity

Question 7

Why might the responder reject positive offers in the ultimatum game? (4)

Answer 7

1. Negative reciprocity
2. Inequality aversion
3. emotions
4. Reputational concerns if the game is repeated

Question 8

What is the utility function of the responder in the ultimatum game if the responder is inequality averse?

Answer 8

Ur (πr,πp) = πr - B(πp - πr)
beta = the disutility from being behind

Question 9

Applying backward induction in the ultimatum game when the responder is inequality averse, what will the proposer do and what will they offer?

Answer 9

Maximise πp so will choose the smallest x that is acceptable to responder. Make the responder indifferent between accepting and rejecting

Question 10

What condition needs to be met for the responder to accept the offer in the ultimatum game if the responder is inequality averse?

Answer 10

𝑥≥𝛽/(1+2𝛽)

Question 11

What will the proposer offer in the ultimatum game when the responder is inequality averse?

Answer 11

𝑥= 𝛽/(1+2𝛽).

Question 12

What is the rollback equilibrium for the ultimatum game with inequality aversion?

Answer 12

Proposer offers 𝑥= 𝛽/(1+2𝛽),
Responder accepts if 𝑥≥ 𝛽/(1+2𝛽) and rejects if 𝑥< 𝛽/(1+2𝛽)
(on the equilibrium path, responder accepts)

Question 13

What are the monetary payoffs for the responder and proposer on the equilibrium path in the ultimatum game with inequality aversion?

Answer 13

𝜋_𝑃=(1+𝛽)/(1+2𝛽), 𝜋_𝑅=𝛽/(1+2𝛽)

Question 14

What are the utilities on the equilibrium path in the ultimatum game with inequality aversion?

Answer 14

𝑢_𝑃= (1+𝛽)/(1+2𝛽), 𝑢_𝑅=0

Question 15

What happens to the proposers offer if the responder is more inequality averse in the ultimatum game ?

Answer 15

it increases

Question 16

What is the centipede game?

Answer 16

Player A can either take £1 or pass it to player B.
If they take 1, B earns nothing
If A passes, experimenter adds 1 more and then player B can pass or take

Question 17

What is the equilibrium outcome in the centipede game when you apply backward induction?

Answer 17

The 1st player takes the money, the other player does not get to move.

Question 18

Why would players pass in the centipede game? (4)

Answer 18

1. Failing to carry out backward induction
2. Altruism: U(£1,£0) < U(£0, £2)
3. Expecting that the opponent will not do backward induction or make mistakes
4. Expecting the opponent will not value rewards

Question 19

What is the trust game?

Answer 19

Player 1 receives £x and decides how much of it to give to player 2. That amount is tripled. Player 2 then decides how much to give back to player 1

Question 20

What is the rollback equilibrium in the trust game?

Answer 20

Player 2 would not return anything - has no incentive too. Player 1 would know this so not give anything to player 2.

Question 21

Why might player 1 send something to player 2 in the trust game? (4)

Answer 21

Altruism or inequality aversion
expecting inequality aversion
expecting positive reciprocity
Player 2 is a friend.

Question 22

Why might player 2 send something to player 1 in the trust game? (3)

Answer 22

Positive reciprocity
inequality aversion
reputational concerns in a repeated