Nash equilibrium
1.[2p] A profile is a Nash equilibrium when
A profile is a Nash equilibrium when
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?
Which of these are true?
Select all that apply
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?
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?
4.[1p] The Nash equilibrium of the prisoner's dilemma is the outcome both players prefer.
The Nash equilibrium of the prisoner's dilemma is the outcome both players prefer.
The answer is: False
5.[2p] Why does the audit game, where the taxpayer prefers to evade when unaudited and to declare when audited, have no pure equilibrium?
Why does the audit game, where the taxpayer prefers to evade when unaudited and to declare when audited, have no pure equilibrium?
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
"Play the equilibrium strategy" is good advice for an individual
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.
What is the term for an agreement that every player would keep out of self-interest once made? Two words.
8.[1p] A strictly dominated strategy can appear in a Nash equilibrium if the payoff difference is small.
A strictly dominated strategy can appear in a Nash equilibrium if the payoff difference is small.
The answer is: False
9.[3p] Match each claim about equilibrium to its status.
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