Lesson test: Coordination and the selection problem

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Coordination and the selection problem

1.[2p]
In battle of the sexes, each player earns 3 at their preferred venue, 1 at the other, and 0 apart. With what probability does a player choose their preferred venue in the mixed equilibrium?

CorrectNot quite: 0.75

2.[3p]
In that same mixed equilibrium, what is the probability the two players end up at the same venue?

CorrectNot quite: 0.375

3.[2p]
The mixed equilibrium of a coordination game pays each player

less than either pure equilibrium, including the one they like least

Correct

more than the worse pure equilibrium but less than the better one

The answer is: less than either pure equilibrium, including the one they like least

the same as the better pure equilibrium

The answer is: less than either pure equilibrium, including the one they like least

an amount that depends on which pure equilibrium is focal

The answer is: less than either pure equilibrium, including the one they like least

4.[3p]
In a stag hunt paying 4 for a joint stag, 3 for a hare whatever the partner does, and 0 for hunting stag alone, what is the minimum probability of the partner hunting stag that makes hunting stag a best response?

CorrectNot quite: 0.75

5.[2p]
In that stag hunt, which equilibrium is risk dominant and which is payoff dominant?

Hare is risk dominant, stag is payoff dominant

Correct

Stag is both

The answer is: Hare is risk dominant, stag is payoff dominant

Hare is both

The answer is: Hare is risk dominant, stag is payoff dominant

Stag is risk dominant, hare is payoff dominant

The answer is: Hare is risk dominant, stag is payoff dominant

6.[3p]
In chicken, swerving against a holder pays -1, holding against a swerver pays 1, mutual swerving pays 0 and a collision pays -10. What is the probability of a collision in the symmetric mixed equilibrium?

CorrectNot quite: 0.01

7.[2p]
Raising the cost of the collision in chicken raises both players' expected payoffs.

True

Correct

False

The answer is: True

8.[3p]
Why is cheap talk effective in a coordination game but useless in a prisoner's dilemma?

In a coordination game a player who announces their move wants to be believed and then matched, so the announcement is credible

Correct

Because coordination games have more equilibria

The answer is: In a coordination game a player who announces their move wants to be believed and then matched, so the announcement is credible

Because players in a coordination game are honest by assumption

The answer is: In a coordination game a player who announces their move wants to be believed and then matched, so the announcement is credible

Because talk changes the payoffs in a coordination game

The answer is: In a coordination game a player who announces their move wants to be believed and then matched, so the announcement is credible

9.[2p]
Match each selection argument to what it appeals to.

Focal point
Risk dominance
Payoff dominance
History

what this group did last time
the best reply to a fifty-fifty belief
conspicuousness that the payoffs do not contain
the equilibrium everyone prefers

Show the answer

Focal point: conspicuousness that the payoffs do not contain Risk dominance: the best reply to a fifty-fifty belief Payoff dominance: the equilibrium everyone prefers History: what this group did last time

1.[2p] In battle of the sexes, each player earns 3 at their preferred venue, 1 at the other, and 0 apart. With what probability does a player choose their preferred venue in the mixed equilibrium?

2.[3p] In that same mixed equilibrium, what is the probability the two players end up at the same venue?

3.[2p] The mixed equilibrium of a coordination game pays each player

4.[3p] In a stag hunt paying 4 for a joint stag, 3 for a hare whatever the partner does, and 0 for hunting stag alone, what is the minimum probability of the partner hunting stag that makes hunting stag a best response?

5.[2p] In that stag hunt, which equilibrium is risk dominant and which is payoff dominant?

6.[3p] In chicken, swerving against a holder pays -1, holding against a swerver pays 1, mutual swerving pays 0 and a collision pays -10. What is the probability of a collision in the symmetric mixed equilibrium?

7.[2p] Raising the cost of the collision in chicken raises both players' expected payoffs.

8.[3p] Why is cheap talk effective in a coordination game but useless in a prisoner's dilemma?

9.[2p] Match each selection argument to what it appeals to.

1.[2p]
In battle of the sexes, each player earns 3 at their preferred venue, 1 at the other, and 0 apart. With what probability does a player choose their preferred venue in the mixed equilibrium?

2.[3p]
In that same mixed equilibrium, what is the probability the two players end up at the same venue?

3.[2p]
The mixed equilibrium of a coordination game pays each player

4.[3p]
In a stag hunt paying 4 for a joint stag, 3 for a hare whatever the partner does, and 0 for hunting stag alone, what is the minimum probability of the partner hunting stag that makes hunting stag a best response?

5.[2p]
In that stag hunt, which equilibrium is risk dominant and which is payoff dominant?

6.[3p]
In chicken, swerving against a holder pays -1, holding against a swerver pays 1, mutual swerving pays 0 and a collision pays -10. What is the probability of a collision in the symmetric mixed equilibrium?

7.[2p]
Raising the cost of the collision in chicken raises both players' expected payoffs.

8.[3p]
Why is cheap talk effective in a coordination game but useless in a prisoner's dilemma?

9.[2p]
Match each selection argument to what it appeals to.