Lesson test: Splitting the surplus

1.[2p]
In the game where both parties simultaneously demand a share of £100 and get nothing if the demands exceed it, how many Nash equilibria are there?

One for every exactly exhausting pair of demands, plus one where both demand everything

Correct

Exactly one, at fifty each

The answer is: One for every exactly exhausting pair of demands, plus one where both demand everything

None, because the payoffs are discontinuous

The answer is: One for every exactly exhausting pair of demands, plus one where both demand everything

Two, one favouring each party

The answer is: One for every exactly exhausting pair of demands, plus one where both demand everything

2.[2p]
What does the Nash bargaining solution maximise?

The product of the two parties' gains over their disagreement payoffs

Correct

The sum of the two parties' utilities

The answer is: The product of the two parties' gains over their disagreement payoffs

The smaller of the two parties' utilities

The answer is: The product of the two parties' gains over their disagreement payoffs

The ratio of the two parties' utilities

The answer is: The product of the two parties' gains over their disagreement payoffs

3.[3p]
Two risk-neutral parties split £100. The first has an outside option worth £30 and the second has none. How much does the first receive, in pounds?

CorrectNot quite: 65

4.[3p]
Two risk-neutral parties split £60, with outside options of £10 and £20. How much does the first receive, in pounds?

CorrectNot quite: 25

5.[3p]
A party with utility $u (x) = \sqrt{x}$ splits £100 with a risk-neutral partner, with no outside options. How much does the risk-averse party receive, in pounds?

CorrectNot quite: 33.33

6.[2p]
Being more risk averse improves a party's share under the Nash bargaining solution.

True

The answer is: False

False

Correct

7.[3p]
Which of these are axioms of the Nash bargaining solution?

Select all that apply

The chosen point is Pareto efficient

Correct

A symmetric problem is solved symmetrically

Correct

The answer is unchanged by rescaling a party's utility affinely

Correct

Removing an option that was not chosen does not change the answer

Correct

The two parties receive equal amounts of money

The answer is: The chosen point is Pareto efficient, A symmetric problem is solved symmetrically, The answer is unchanged by rescaling a party's utility affinely, Removing an option that was not chosen does not change the answer

8.[3p]
Which axiom does the Kalai-Smorodinsky solution replace, and with what?

Independence of irrelevant alternatives, replaced by monotonicity

Correct

Symmetry, replaced by proportionality

The answer is: Independence of irrelevant alternatives, replaced by monotonicity

Efficiency, replaced by fairness

The answer is: Independence of irrelevant alternatives, replaced by monotonicity

Affine invariance, replaced by comparability

The answer is: Independence of irrelevant alternatives, replaced by monotonicity

9.[3p]
The frontier is $x + 2 y = 120$ with disagreement at the origin and both parties risk neutral. What is $x$ at the Nash solution?

CorrectNot quite: 60

1.[2p] In the game where both parties simultaneously demand a share of £100 and get nothing if the demands exceed it, how many Nash equilibria are there?

2.[2p] What does the Nash bargaining solution maximise?

3.[3p] Two risk-neutral parties split £100. The first has an outside option worth £30 and the second has none. How much does the first receive, in pounds?

4.[3p] Two risk-neutral parties split £60, with outside options of £10 and £20. How much does the first receive, in pounds?

5.[3p] A party with utility u(x)=x splits £100 with a risk-neutral partner, with no outside options. How much does the risk-averse party receive, in pounds?

6.[2p] Being more risk averse improves a party's share under the Nash bargaining solution.

7.[3p] Which of these are axioms of the Nash bargaining solution?

8.[3p] Which axiom does the Kalai-Smorodinsky solution replace, and with what?

9.[3p] The frontier is x+2y=120 with disagreement at the origin and both parties risk neutral. What is x at the Nash solution?

1.[2p]
In the game where both parties simultaneously demand a share of £100 and get nothing if the demands exceed it, how many Nash equilibria are there?

2.[2p]
What does the Nash bargaining solution maximise?

3.[3p]
Two risk-neutral parties split £100. The first has an outside option worth £30 and the second has none. How much does the first receive, in pounds?

4.[3p]
Two risk-neutral parties split £60, with outside options of £10 and £20. How much does the first receive, in pounds?

5.[3p]
A party with utility $u (x) = \sqrt{x}$ splits £100 with a risk-neutral partner, with no outside options. How much does the risk-averse party receive, in pounds?

6.[2p]
Being more risk averse improves a party's share under the Nash bargaining solution.

7.[3p]
Which of these are axioms of the Nash bargaining solution?

8.[3p]
Which axiom does the Kalai-Smorodinsky solution replace, and with what?

9.[3p]
The frontier is $x + 2 y = 120$ with disagreement at the origin and both parties risk neutral. What is $x$ at the Nash solution?