Lesson test: Where the predictions fail

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Where the predictions fail

1.[2p]
In the beauty contest where the target is two thirds of the average, what is the unique Nash equilibrium?

Everyone chooses 0

Correct

Everyone chooses 33

The answer is: Everyone chooses 0

Everyone chooses 50

The answer is: Everyone chooses 0

There is no equilibrium in pure strategies

The answer is: Everyone chooses 0

2.[3p]
With a target of two thirds of the average and level-0 players averaging 50, what does a level-2 player choose?

CorrectNot quite: 22.2

3.[3p]
What does a level-k player believe about the other players?

That they all reason to a strictly lower level than themselves

Correct

That they are all playing the Nash equilibrium

The answer is: That they all reason to a strictly lower level than themselves

That they are all choosing at random

The answer is: That they all reason to a strictly lower level than themselves

That they know the level-k player's own level

The answer is: That they all reason to a strictly lower level than themselves

4.[3p]
Two actions pay 5 and 4. In a logit quantal response with precision $λ = 1$ , what is the probability of choosing the better one?

CorrectNot quite: 0.731

5.[2p]
What happens to quantal response equilibrium as the precision parameter goes to infinity?

It converges to Nash equilibrium

Correct

It converges to uniformly random play

The answer is: It converges to Nash equilibrium

It converges to the maximin strategy

The answer is: It converges to Nash equilibrium

It ceases to exist

The answer is: It converges to Nash equilibrium

6.[3p]
A Fehr-Schmidt responder with envy parameter $α = 0.5$ faces a £10 pie. What is the smallest offer, in pounds, that they accept?

CorrectNot quite: 2.5

7.[3p]
In which settings does game theory have a good empirical record?

Select all that apply

Penalty kick and tennis serve direction among professionals

Correct

Bidding behaviour in large auctions

Correct

Ultimatum game offers and rejections

The answer is: Penalty kick and tennis serve direction among professionals, Bidding behaviour in large auctions, Designing matching procedures such as medical residency assignment

Predicting the first move in the centipede game

The answer is: Penalty kick and tennis serve direction among professionals, Bidding behaviour in large auctions, Designing matching procedures such as medical residency assignment

Designing matching procedures such as medical residency assignment

Correct

8.[2p]
A model that explains an anomaly by adding a preference parameter fitted separately to each game is making a testable prediction.

True

The answer is: False

False

Correct

9.[2p]
Match each model to the assumption it drops.

Level-k
Quantal response
Inequity aversion
Cognitive hierarchy

always choosing the best action
payoffs equal to own money
best responding to one level alone
common knowledge of rationality

Show the answer

Level-k: common knowledge of rationality Quantal response: always choosing the best action Inequity aversion: payoffs equal to own money Cognitive hierarchy: best responding to one level alone

1.[2p] In the beauty contest where the target is two thirds of the average, what is the unique Nash equilibrium?

2.[3p] With a target of two thirds of the average and level-0 players averaging 50, what does a level-2 player choose?

3.[3p] What does a level-k player believe about the other players?

4.[3p] Two actions pay 5 and 4. In a logit quantal response with precision λ=1, what is the probability of choosing the better one?

5.[2p] What happens to quantal response equilibrium as the precision parameter goes to infinity?

6.[3p] A Fehr-Schmidt responder with envy parameter α=0.5 faces a £10 pie. What is the smallest offer, in pounds, that they accept?

7.[3p] In which settings does game theory have a good empirical record?

8.[2p] A model that explains an anomaly by adding a preference parameter fitted separately to each game is making a testable prediction.

9.[2p] Match each model to the assumption it drops.

1.[2p]
In the beauty contest where the target is two thirds of the average, what is the unique Nash equilibrium?

2.[3p]
With a target of two thirds of the average and level-0 players averaging 50, what does a level-2 player choose?

3.[3p]
What does a level-k player believe about the other players?

4.[3p]
Two actions pay 5 and 4. In a logit quantal response with precision $λ = 1$ , what is the probability of choosing the better one?

5.[2p]
What happens to quantal response equilibrium as the precision parameter goes to infinity?

6.[3p]
A Fehr-Schmidt responder with envy parameter $α = 0.5$ faces a £10 pie. What is the smallest offer, in pounds, that they accept?

7.[3p]
In which settings does game theory have a good empirical record?

8.[2p]
A model that explains an anomaly by adding a preference parameter fitted separately to each game is making a testable prediction.

9.[2p]
Match each model to the assumption it drops.