Lesson test: The folk theorem

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The folk theorem

1.[2p]
What does the folk theorem say about the infinitely repeated game?

Every feasible payoff vector strictly above the minmax is an equilibrium payoff once players are patient enough

Correct

Mutual cooperation is the unique equilibrium once players are patient enough

The answer is: Every feasible payoff vector strictly above the minmax is an equilibrium payoff once players are patient enough

Repetition removes all equilibria except the stage game's

The answer is: Every feasible payoff vector strictly above the minmax is an equilibrium payoff once players are patient enough

The repeated game has no equilibrium unless the horizon is finite

The answer is: Every feasible payoff vector strictly above the minmax is an equilibrium payoff once players are patient enough

2.[3p]
What is a player's minmax value?

The least the other players can hold them to when they best respond

Correct

The most they can guarantee themselves when they must move first

The answer is: The least the other players can hold them to when they best respond

Their payoff in the worst Nash equilibrium

The answer is: The least the other players can hold them to when they best respond

The average of their payoffs across the payoff table

The answer is: The least the other players can hold them to when they best respond

3.[3p]
Player 1 earns 4 from row T against L and 0 against R, and 0 from row B against L and 3 against R. What is player 1's minmax value when player 2 may randomise?

CorrectNot quite: 1.71

4.[2p]
Allowing the punishing players to randomise can lower a player's minmax value below what any pure punishment achieves.

True

Correct

False

The answer is: True

5.[2p]
In the prisoner's dilemma with $T = 6$ , $R = 4$ , $P = 2$ , $S = 1$ , what is each player's minmax value?

CorrectNot quite: 2

6.[3p]
Why is the folk theorem a problem rather than a triumph?

The set of equilibrium payoffs is so large that no observation could contradict the model

Correct

Its proof requires an infinite horizon, which no real relationship has

The answer is: The set of equilibrium payoffs is so large that no observation could contradict the model

It contradicts the existence theorem for Nash equilibrium

The answer is: The set of equilibrium payoffs is so large that no observation could contradict the model

It shows cooperation is impossible without contracts

The answer is: The set of equilibrium payoffs is so large that no observation could contradict the model

7.[3p]
Which of these were true of tit for tat in Axelrod's tournaments?

Select all that apply

It won both tournaments on total score

Correct

It was the shortest program submitted

Correct

It never scored more than an opponent in a head-to-head match

Correct

It performs poorly when moves are occasionally misread

Correct

It won every head-to-head match it played

The answer is: It won both tournaments on total score, It was the shortest program submitted, It never scored more than an opponent in a head-to-head match, It performs poorly when moves are occasionally misread

8.[3p]
With Axelrod's scoring, $T = 5$ , $R = 3$ , $P = 1$ , $S = 0$ , what does tit for tat score against unconditional defection over 200 rounds?

CorrectNot quite: 199

9.[2p]
Match each strategy or result to what it does.

Grim trigger
Generous tit for tat
Win-stay lose-shift
Zero-determinant

punishes any defection forever
fixes a ratio between the two scores
repeats a move that worked
forgives some defections at random

Show the answer

Grim trigger: punishes any defection forever Generous tit for tat: forgives some defections at random Win-stay lose-shift: repeats a move that worked Zero-determinant: fixes a ratio between the two scores

1.[2p] What does the folk theorem say about the infinitely repeated game?

2.[3p] What is a player's minmax value?

3.[3p] Player 1 earns 4 from row T against L and 0 against R, and 0 from row B against L and 3 against R. What is player 1's minmax value when player 2 may randomise?

4.[2p] Allowing the punishing players to randomise can lower a player's minmax value below what any pure punishment achieves.

5.[2p] In the prisoner's dilemma with T=6, R=4, P=2, S=1, what is each player's minmax value?

6.[3p] Why is the folk theorem a problem rather than a triumph?

7.[3p] Which of these were true of tit for tat in Axelrod's tournaments?

8.[3p] With Axelrod's scoring, T=5, R=3, P=1, S=0, what does tit for tat score against unconditional defection over 200 rounds?

9.[2p] Match each strategy or result to what it does.

1.[2p]
What does the folk theorem say about the infinitely repeated game?

2.[3p]
What is a player's minmax value?

3.[3p]
Player 1 earns 4 from row T against L and 0 against R, and 0 from row B against L and 3 against R. What is player 1's minmax value when player 2 may randomise?

4.[2p]
Allowing the punishing players to randomise can lower a player's minmax value below what any pure punishment achieves.

5.[2p]
In the prisoner's dilemma with $T = 6$ , $R = 4$ , $P = 2$ , $S = 1$ , what is each player's minmax value?

6.[3p]
Why is the folk theorem a problem rather than a triumph?

7.[3p]
Which of these were true of tit for tat in Axelrod's tournaments?

8.[3p]
With Axelrod's scoring, $T = 5$ , $R = 3$ , $P = 1$ , $S = 0$ , what does tit for tat score against unconditional defection over 200 rounds?

9.[2p]
Match each strategy or result to what it does.