Lesson test: Dominance

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Dominance

1.[2p]
Strategy $s_{i}'$ strictly dominates $s_{i}$ when

$s_{i}'$ pays strictly more than $s_{i}$ against every combination of the others' strategies

Correct

$s_{i}'$ pays strictly more than $s_{i}$ against the opponent's equilibrium strategy

The answer is: $s_{i}'$ pays strictly more than $s_{i}$ against every combination of the others' strategies

$s_{i}'$ pays at least as much as $s_{i}$ everywhere and more somewhere

The answer is: $s_{i}'$ pays strictly more than $s_{i}$ against every combination of the others' strategies

$s_{i}'$ has the highest payoff anywhere in the table

The answer is: $s_{i}'$ pays strictly more than $s_{i}$ against every combination of the others' strategies

2.[3p]
Which statements about strictly dominated strategies are correct?

Select all that apply

A strictly dominated strategy is a best reply to no belief whatsoever about the opponent

Correct

Deleting strictly dominated strategies in different orders leaves the same survivors

Correct

A strategy can be strictly dominated by a mixture while no single strategy dominates it

Correct

A rational player might still play one if the payoff difference is small

The answer is: A strictly dominated strategy is a best reply to no belief whatsoever about the opponent, Deleting strictly dominated strategies in different orders leaves the same survivors, A strategy can be strictly dominated by a mixture while no single strategy dominates it

3.[2p]
A game has $T = 6$ , $R = 4$ , $P = 2$ , $S = 1$ . What is $2 R - (T + S)$ ?

CorrectNot quite: 1

4.[2p]
A game with $T = 7$ , $R = 3$ , $P = 1$ , $S = 0$ satisfies the condition that mutual cooperation beats alternating exploitation.

True

The answer is: False

False

Correct

5.[2p]
In the game where U, M, D face L, C, R, put the three deletions in the order they become legal.

Rows M and D, dominated by row U
Column R, dominated by column L
Column C, dominated by column R

Show the answer

a, b, c

6.[2p]
Deleting a strategy at the third round of iterated deletion requires

more levels of knowledge about others' rationality than the first round does

Correct

exactly the same assumptions as the first round

The answer is: more levels of knowledge about others' rationality than the first round does

that the game be zero-sum

The answer is: more levels of knowledge about others' rationality than the first round does

that both players have a dominant strategy

The answer is: more levels of knowledge about others' rationality than the first round does

7.[3p]
Row U pays 6 against L and 0 against R; row D pays 0 against L and 6 against R; row M pays the same amount $x$ in both columns. Strictly below what value of $x$ is M strictly dominated by a mixture of U and D?

CorrectNot quite: 3

8.[2p]
Iterated deletion of weakly dominated strategies can leave different survivors depending on the order of deletion.

True

Correct

False

The answer is: True

9.[2p]
Match each payoff label in a prisoner's dilemma to what it pays.

defecting alone against a cooperator
cooperating alone against a defector
both players defecting
both players cooperating

Show the answer

T: defecting alone against a cooperator R: both players cooperating P: both players defecting S: cooperating alone against a defector

1.[2p] Strategy si′ strictly dominates si when

2.[3p] Which statements about strictly dominated strategies are correct?

3.[2p] A game has T=6, R=4, P=2, S=1. What is 2R−(T+S)?

4.[2p] A game with T=7, R=3, P=1, S=0 satisfies the condition that mutual cooperation beats alternating exploitation.

5.[2p] In the game where U, M, D face L, C, R, put the three deletions in the order they become legal.

6.[2p] Deleting a strategy at the third round of iterated deletion requires

7.[3p] Row U pays 6 against L and 0 against R; row D pays 0 against L and 6 against R; row M pays the same amount x in both columns. Strictly below what value of x is M strictly dominated by a mixture of U and D?

8.[2p] Iterated deletion of weakly dominated strategies can leave different survivors depending on the order of deletion.

9.[2p] Match each payoff label in a prisoner's dilemma to what it pays.

1.[2p]
Strategy $s_{i}'$ strictly dominates $s_{i}$ when

2.[3p]
Which statements about strictly dominated strategies are correct?

3.[2p]
A game has $T = 6$ , $R = 4$ , $P = 2$ , $S = 1$ . What is $2 R - (T + S)$ ?

4.[2p]
A game with $T = 7$ , $R = 3$ , $P = 1$ , $S = 0$ satisfies the condition that mutual cooperation beats alternating exploitation.

5.[2p]
In the game where U, M, D face L, C, R, put the three deletions in the order they become legal.

6.[2p]
Deleting a strategy at the third round of iterated deletion requires

7.[3p]
Row U pays 6 against L and 0 against R; row D pays 0 against L and 6 against R; row M pays the same amount $x$ in both columns. Strictly below what value of $x$ is M strictly dominated by a mixture of U and D?

8.[2p]
Iterated deletion of weakly dominated strategies can leave different survivors depending on the order of deletion.

9.[2p]
Match each payoff label in a prisoner's dilemma to what it pays.