Lesson test: Repetition and the shadow of the future

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Repetition and the shadow of the future

1.[2p]
Why does cooperation unravel in a prisoner's dilemma repeated a known twenty times?

The last round has no future to protect, so it is settled regardless of history, and that makes the nineteenth unconditional too

Correct

Twenty rounds is too few for a reputation to form

The answer is: The last round has no future to protect, so it is settled regardless of history, and that makes the nineteenth unconditional too

The players discount the future too heavily over twenty rounds

The answer is: The last round has no future to protect, so it is settled regardless of history, and that makes the nineteenth unconditional too

Mutual defection is Pareto efficient in the repeated game

The answer is: The last round has no future to protect, so it is settled regardless of history, and that makes the nineteenth unconditional too

2.[2p]
A relationship continues each period with probability 0.95 and the interest rate per period is 5 per cent. What is the discount factor?

CorrectNot quite: 0.905

3.[2p]
A player earns 20 every period forever, with a discount factor of 0.8. What is the present value of that stream?

CorrectNot quite: 100

4.[3p]
A stage game has $T = 9$ , $R = 6$ , $P = 1$ and $S = 0$ . What is the smallest discount factor at which grim trigger sustains cooperation?

CorrectNot quite: 0.375

5.[2p]
The sucker's payoff $S$ appears in the grim trigger threshold.

True

The answer is: False

False

Correct

6.[3p]
In any symmetric Cournot duopoly with linear demand and constant marginal cost, what discount factor does grim trigger need to hold the full cartel? Give it as a decimal.

CorrectNot quite: 0.529

7.[3p]
Why does tit for tat require more patience than grim trigger in the same stage game?

Its punishment ends, so a player can profit by alternating defection with cooperation

Correct

Its punishment is harsher, so it is less credible

The answer is: Its punishment ends, so a player can profit by alternating defection with cooperation

It starts by defecting rather than cooperating

The answer is: Its punishment ends, so a player can profit by alternating defection with cooperation

It cannot be written as a strategy in the repeated game

The answer is: Its punishment ends, so a player can profit by alternating defection with cooperation

8.[3p]
Which of these does the repeated-game argument for cooperation actually require?

Select all that apply

That defections are observed by the other player

Correct

That there is no commonly known final round

Correct

That the same players meet again and are recognised

Correct

That at least one player has preferences over the other's welfare

The answer is: That defections are observed by the other player, That there is no commonly known final round, That the same players meet again and are recognised

That the players can sign an enforceable contract

The answer is: That defections are observed by the other player, That there is no commonly known final round, That the same players meet again and are recognised

9.[2p]
Match each quantity to what it measures.

$1 / (1 - δ)$
$T - R$
$T - P$
$δ^{k}$

patience needed with a detection lag
the one-period gain from cheating
the per-period loss after punishment
expected length of the relationship

Show the answer

$1 / (1 - δ)$ : expected length of the relationship $T - R$ : the one-period gain from cheating $T - P$ : the per-period loss after punishment $δ^{k}$ : patience needed with a detection lag

1.[2p] Why does cooperation unravel in a prisoner's dilemma repeated a known twenty times?

2.[2p] A relationship continues each period with probability 0.95 and the interest rate per period is 5 per cent. What is the discount factor?

3.[2p] A player earns 20 every period forever, with a discount factor of 0.8. What is the present value of that stream?

4.[3p] A stage game has T=9, R=6, P=1 and S=0. What is the smallest discount factor at which grim trigger sustains cooperation?

5.[2p] The sucker's payoff S appears in the grim trigger threshold.

6.[3p] In any symmetric Cournot duopoly with linear demand and constant marginal cost, what discount factor does grim trigger need to hold the full cartel? Give it as a decimal.

7.[3p] Why does tit for tat require more patience than grim trigger in the same stage game?

8.[3p] Which of these does the repeated-game argument for cooperation actually require?

9.[2p] Match each quantity to what it measures.

1.[2p]
Why does cooperation unravel in a prisoner's dilemma repeated a known twenty times?

2.[2p]
A relationship continues each period with probability 0.95 and the interest rate per period is 5 per cent. What is the discount factor?

3.[2p]
A player earns 20 every period forever, with a discount factor of 0.8. What is the present value of that stream?

4.[3p]
A stage game has $T = 9$ , $R = 6$ , $P = 1$ and $S = 0$ . What is the smallest discount factor at which grim trigger sustains cooperation?

5.[2p]
The sucker's payoff $S$ appears in the grim trigger threshold.

6.[3p]
In any symmetric Cournot duopoly with linear demand and constant marginal cost, what discount factor does grim trigger need to hold the full cartel? Give it as a decimal.

7.[3p]
Why does tit for tat require more patience than grim trigger in the same stage game?

8.[3p]
Which of these does the repeated-game argument for cooperation actually require?

9.[2p]
Match each quantity to what it measures.