Lesson test: Zero-sum games and minimax

1.[2p]
In a zero-sum game, the relation between maximin and minimax in pure strategies is

maximin is always less than or equal to minimax

Correct

maximin is always greater than or equal to minimax

The answer is: maximin is always less than or equal to minimax

they are always equal

The answer is: maximin is always less than or equal to minimax

there is no general relation

The answer is: maximin is always less than or equal to minimax

4.[3p]
A zero-sum game pays the row player 3 and -1 in the top row and -2 and 2 in the bottom. What is the value of the game?

CorrectNot quite: 0.5

5.[3p]
In that same game, with what probability does the column player choose the left column in equilibrium?

CorrectNot quite: 0.375

6.[3p]
Which properties hold in every finite two-player zero-sum game but not in general games?

Select all that apply

All equilibria give the same payoffs

Correct

Equilibrium strategies are interchangeable across equilibria

Correct

A player's equilibrium strategy is also their security strategy

Correct

An equilibrium in pure strategies always exists

The answer is: All equilibria give the same payoffs, Equilibrium strategies are interchangeable across equilibria, A player's equilibrium strategy is also their security strategy

7.[3p]
Penalty scoring rates are 58.30 and 94.97 per cent when the kicker goes left against a keeper diving left or right, and 92.91 and 69.92 per cent when the kicker goes right. What fraction of kicks should go left in equilibrium?

CorrectNot quite: 0.385

8.[2p]
Equilibrium in the penalty game requires only that the overall frequencies be right, not that successive kicks be independent.

True

The answer is: False

False

Correct

9.[2p]
Which is the strongest reason "treat this negotiation as zero-sum" is usually a mistake?

Most negotiations contain gains from agreement, so the payoffs do not add to a constant

Correct

Zero-sum games have no equilibrium

The answer is: Most negotiations contain gains from agreement, so the payoffs do not add to a constant

Zero-sum games cannot be solved without a computer

The answer is: Most negotiations contain gains from agreement, so the payoffs do not add to a constant

The minimax theorem applies only to games with more than two players

The answer is: Most negotiations contain gains from agreement, so the payoffs do not add to a constant

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Zero-sum games and minimax

1.[2p]
In a zero-sum game, the relation between maximin and minimax in pure strategies is

2.[2p]
A zero-sum game has row payoffs 6, 2, 3 in the top row and 1, 4, 5 in the bottom. What is the maximin?

3.[2p]
For the same game, what is the minimax?

4.[3p]
A zero-sum game pays the row player 3 and -1 in the top row and -2 and 2 in the bottom. What is the value of the game?

5.[3p]
In that same game, with what probability does the column player choose the left column in equilibrium?

6.[3p]
Which properties hold in every finite two-player zero-sum game but not in general games?

7.[3p]
Penalty scoring rates are 58.30 and 94.97 per cent when the kicker goes left against a keeper diving left or right, and 92.91 and 69.92 per cent when the kicker goes right. What fraction of kicks should go left in equilibrium?

8.[2p]
Equilibrium in the penalty game requires only that the overall frequencies be right, not that successive kicks be independent.

9.[2p]
Which is the strongest reason "treat this negotiation as zero-sum" is usually a mistake?

1.[2p] In a zero-sum game, the relation between maximin and minimax in pure strategies is

2.[2p] A zero-sum game has row payoffs 6, 2, 3 in the top row and 1, 4, 5 in the bottom. What is the maximin?

3.[2p] For the same game, what is the minimax?

4.[3p] A zero-sum game pays the row player 3 and -1 in the top row and -2 and 2 in the bottom. What is the value of the game?

5.[3p] In that same game, with what probability does the column player choose the left column in equilibrium?

6.[3p] Which properties hold in every finite two-player zero-sum game but not in general games?

7.[3p] Penalty scoring rates are 58.30 and 94.97 per cent when the kicker goes left against a keeper diving left or right, and 92.91 and 69.92 per cent when the kicker goes right. What fraction of kicks should go left in equilibrium?

8.[2p] Equilibrium in the penalty game requires only that the overall frequencies be right, not that successive kicks be independent.

9.[2p] Which is the strongest reason "treat this negotiation as zero-sum" is usually a mistake?

1.[2p]
In a zero-sum game, the relation between maximin and minimax in pure strategies is

2.[2p]
A zero-sum game has row payoffs 6, 2, 3 in the top row and 1, 4, 5 in the bottom. What is the maximin?

3.[2p]
For the same game, what is the minimax?

4.[3p]
A zero-sum game pays the row player 3 and -1 in the top row and -2 and 2 in the bottom. What is the value of the game?

5.[3p]
In that same game, with what probability does the column player choose the left column in equilibrium?

6.[3p]
Which properties hold in every finite two-player zero-sum game but not in general games?

7.[3p]
Penalty scoring rates are 58.30 and 94.97 per cent when the kicker goes left against a keeper diving left or right, and 92.91 and 69.92 per cent when the kicker goes right. What fraction of kicks should go left in equilibrium?

8.[2p]
Equilibrium in the penalty game requires only that the overall frequencies be right, not that successive kicks be independent.

9.[2p]
Which is the strongest reason "treat this negotiation as zero-sum" is usually a mistake?