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Nash equilibrium

Nash equilibrium

1.[2p]

A profile is a Nash equilibrium when

Correct
The answer is: no player can raise their own payoff by changing their own strategy alone
The answer is: no player can raise their own payoff by changing their own strategy alone
The answer is: no player can raise their own payoff by changing their own strategy alone

2.[3p]

Which of these are true?

Select all that apply

Correct
Correct
Correct
The answer is: If every player has a strictly dominant strategy, that profile is the unique Nash equilibrium, Iterated deletion of strictly dominated strategies never removes an equilibrium strategy, A game can have more than one Nash equilibrium

3.[3p]

In the grid with rows T, M, B and columns L, C, R holding payoffs 3,1 / 0,2 / 5,0 across the top row, 2,3 / 4,4 / 1,2 in the middle, and 1,0 / 3,1 / 6,5 at the bottom, how many pure-strategy equilibria are there?

CorrectNot quite: 2

4.[1p]

The Nash equilibrium of the prisoner's dilemma is the outcome both players prefer.

The answer is: False
Correct

5.[2p]

Why does the audit game, where the taxpayer prefers to evade when unaudited and to declare when audited, have no pure equilibrium?

Correct
The answer is: The best responses form a closed cycle, so every cell has one player who wants to move
The answer is: The best responses form a closed cycle, so every cell has one player who wants to move
The answer is: The best responses form a closed cycle, so every cell has one player who wants to move

6.[2p]

"Play the equilibrium strategy" is good advice for an individual

Correct
The answer is: only when the others are playing theirs, since against a predictable opponent a better reply usually exists
The answer is: only when the others are playing theirs, since against a predictable opponent a better reply usually exists
The answer is: only when the others are playing theirs, since against a predictable opponent a better reply usually exists

7.[2p]

What is the term for an agreement that every player would keep out of self-interest once made? Two words.

CorrectNot quite: self-enforcing agreement

8.[1p]

A strictly dominated strategy can appear in a Nash equilibrium if the payoff difference is small.

The answer is: False
Correct

9.[3p]

Match each claim about equilibrium to its status.

  • Every player is best-responding

  • Nobody regrets their own choice

  • The outcome is efficient

  • There is exactly one

  • false in many games

  • an equivalent statement

  • part of the definition

  • false in the prisoner's dilemma

Show the answer

Every player is best-responding: part of the definition Nobody regrets their own choice: an equivalent statement The outcome is efficient: false in the prisoner's dilemma There is exactly one: false in many games