Lesson test: Bargaining by taking turns

Sign in

Libre University uses your GitHub account. Signing in is only needed to sit a final test, so the score is kept on your profile.

Bargaining by taking turns

1.[2p]
What is the subgame perfect outcome of the one-shot ultimatum game?

The proposer keeps everything but the smallest positive amount, and the offer is accepted

Correct

The two parties split the pie evenly

The answer is: The proposer keeps everything but the smallest positive amount, and the offer is accepted

The responder rejects, since the offer is unfair

The answer is: The proposer keeps everything but the smallest positive amount, and the offer is accepted

There is no subgame perfect equilibrium

The answer is: The proposer keeps everything but the smallest positive amount, and the offer is accepted

2.[3p]
In Rubinstein's infinite alternating-offers game with a common discount factor of 0.9, what fraction of the pie does the first proposer keep?

CorrectNot quite: 0.526

3.[3p]
Same game, but the common discount factor is 0.5. What fraction does the first proposer keep?

CorrectNot quite: 0.667

4.[3p]
Party 1 discounts at 0.9 per round and party 2 at 0.8, and party 1 proposes first. What fraction does party 1 receive?

CorrectNot quite: 0.714

5.[2p]
In the subgame perfect equilibrium of Rubinstein's model, agreement is reached in the first period.

True

Correct

False

The answer is: True

6.[3p]
As the interval between offers shrinks to zero, party 1's share converges to

$r_{2} / (r_{1} + r_{2})$ , so it depends only on the ratio of the two impatience rates

Correct

one half, whatever the discount rates

The answer is: $r_2/(r_1 + r_2)$, so it depends only on the ratio of the two impatience rates

the whole pie, since the first mover advantage grows

The answer is: $r_2/(r_1 + r_2)$, so it depends only on the ratio of the two impatience rates

zero, since delay becomes costless

The answer is: $r_2/(r_1 + r_2)$, so it depends only on the ratio of the two impatience rates

7.[3p]
Which of these are established findings from ultimatum game experiments?

Select all that apply

The modal offer is close to half the pie

Correct

Offers below about a fifth are frequently rejected

Correct

Behaviour varies sharply between societies

Correct

Raising the stakes to several months of income makes subjects play the theoretical prediction

The answer is: The modal offer is close to half the pie, Offers below about a fifth are frequently rejected, Behaviour varies sharply between societies

8.[3p]
What did Ochs and Roth mean by a disadvantageous counter-offer?

A rejecting party countered with a demand worth less to them than what they had refused

Correct

A party offered more than the equilibrium share

The answer is: A rejecting party countered with a demand worth less to them than what they had refused

A party made two offers in the same period

The answer is: A rejecting party countered with a demand worth less to them than what they had refused

A party accepted an offer worth less than their outside option

The answer is: A rejecting party countered with a demand worth less to them than what they had refused

9.[2p]
Put the steps of the Rubinstein argument in order.

The proposer offers exactly $δ x$ and keeps $1 - δ x$
Setting that equal to $x$ gives $x = 1 / (1 + δ)$
Every subgame in which a given player proposes looks the same, so their share is the same $x$
A responder can reject and propose next period, which is worth $δ x$ to them

Show the answer

a, b, c, d

1.[2p] What is the subgame perfect outcome of the one-shot ultimatum game?

2.[3p] In Rubinstein's infinite alternating-offers game with a common discount factor of 0.9, what fraction of the pie does the first proposer keep?

3.[3p] Same game, but the common discount factor is 0.5. What fraction does the first proposer keep?

4.[3p] Party 1 discounts at 0.9 per round and party 2 at 0.8, and party 1 proposes first. What fraction does party 1 receive?

5.[2p] In the subgame perfect equilibrium of Rubinstein's model, agreement is reached in the first period.

6.[3p] As the interval between offers shrinks to zero, party 1's share converges to

7.[3p] Which of these are established findings from ultimatum game experiments?

8.[3p] What did Ochs and Roth mean by a disadvantageous counter-offer?

9.[2p] Put the steps of the Rubinstein argument in order.

1.[2p]
What is the subgame perfect outcome of the one-shot ultimatum game?

2.[3p]
In Rubinstein's infinite alternating-offers game with a common discount factor of 0.9, what fraction of the pie does the first proposer keep?

3.[3p]
Same game, but the common discount factor is 0.5. What fraction does the first proposer keep?

4.[3p]
Party 1 discounts at 0.9 per round and party 2 at 0.8, and party 1 proposes first. What fraction does party 1 receive?

5.[2p]
In the subgame perfect equilibrium of Rubinstein's model, agreement is reached in the first period.

6.[3p]
As the interval between offers shrinks to zero, party 1's share converges to

7.[3p]
Which of these are established findings from ultimatum game experiments?

8.[3p]
What did Ochs and Roth mean by a disadvantageous counter-offer?

9.[2p]
Put the steps of the Rubinstein argument in order.