Lesson test: What a game is

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What a game is

1.[2p]
What distinguishes a game from an ordinary decision problem?

The payoff to your choice depends on choices made by others who are reasoning about you

Correct

The outcome is uncertain

The answer is: The payoff to your choice depends on choices made by others who are reasoning about you

There is more than one possible action

The answer is: The payoff to your choice depends on choices made by others who are reasoning about you

The players are competing rather than cooperating

The answer is: The payoff to your choice depends on choices made by others who are reasoning about you

2.[1p]
In a cell written 10.2, 2.7, which payoff belongs to whom?

10.2 is the row player's and 2.7 is the column player's

Correct

2.7 is the row player's and 10.2 is the column player's

The answer is: 10.2 is the row player's and 2.7 is the column player's

The larger number always belongs to the player who moved first

The answer is: 10.2 is the row player's and 2.7 is the column player's

The order is arbitrary and must be stated for each table

The answer is: 10.2 is the row player's and 2.7 is the column player's

3.[2p]
Two airlines split 200 passengers evenly at equal fares, and an undercutter takes 170. A fare of £120 or £90 faces a cost of £50 per passenger. If A charges £90 and B charges £120, what is A's profit in pounds?

CorrectNot quite: 6800

4.[3p]
A player with utility $u (m) = \sqrt{m}$ faces a coin flip between £25 and £225. What certain sum in pounds is that gamble worth to them?

CorrectNot quite: 100

5.[2p]
Which changes to one player's payoff numbers leave the game strategically identical?

Select all that apply

Multiplying every payoff by 2

Correct

Adding 7 to every payoff

Correct

Squaring every payoff

The answer is: Multiplying every payoff by 2, Adding 7 to every payoff

Multiplying every payoff by -1

The answer is: Multiplying every payoff by 2, Adding 7 to every payoff

6.[1p]
A cell reading 9.0, 9.0 tells you the two players are equally well off.

True

The answer is: False

False

Correct

7.[1p]
A game has three players, with 3, 4 and 2 strategies respectively. How many strategy profiles does it have?

CorrectNot quite: 24

8.[2p]
Common knowledge of the game means

everyone knows the game, everyone knows that everyone knows, and so on without limit

Correct

everyone happens to know the payoffs

The answer is: everyone knows the game, everyone knows that everyone knows, and so on without limit

the players have agreed on the rules in advance

The answer is: everyone knows the game, everyone knows that everyone knows, and so on without limit

the payoffs are public information published somewhere

The answer is: everyone knows the game, everyone knows that everyone knows, and so on without limit

9.[3p]
Match each term to what it names.

Strategy profile
Payoff function
Normal form
Strategy

players, strategy sets and payoffs
one strategy chosen for every player
a number for each complete profile
a complete contingent plan of action

Show the answer

Strategy profile: one strategy chosen for every player Payoff function: a number for each complete profile Normal form: players, strategy sets and payoffs Strategy: a complete contingent plan of action

1.[2p] What distinguishes a game from an ordinary decision problem?

2.[1p] In a cell written 10.2, 2.7, which payoff belongs to whom?

3.[2p] Two airlines split 200 passengers evenly at equal fares, and an undercutter takes 170. A fare of £120 or £90 faces a cost of £50 per passenger. If A charges £90 and B charges £120, what is A's profit in pounds?

4.[3p] A player with utility u(m)=m faces a coin flip between £25 and £225. What certain sum in pounds is that gamble worth to them?

5.[2p] Which changes to one player's payoff numbers leave the game strategically identical?

6.[1p] A cell reading 9.0, 9.0 tells you the two players are equally well off.

7.[1p] A game has three players, with 3, 4 and 2 strategies respectively. How many strategy profiles does it have?

8.[2p] Common knowledge of the game means

9.[3p] Match each term to what it names.

1.[2p]
What distinguishes a game from an ordinary decision problem?

2.[1p]
In a cell written 10.2, 2.7, which payoff belongs to whom?

3.[2p]
Two airlines split 200 passengers evenly at equal fares, and an undercutter takes 170. A fare of £120 or £90 faces a cost of £50 per passenger. If A charges £90 and B charges £120, what is A's profit in pounds?

4.[3p]
A player with utility $u (m) = \sqrt{m}$ faces a coin flip between £25 and £225. What certain sum in pounds is that gamble worth to them?

5.[2p]
Which changes to one player's payoff numbers leave the game strategically identical?

6.[1p]
A cell reading 9.0, 9.0 tells you the two players are equally well off.

7.[1p]
A game has three players, with 3, 4 and 2 strategies respectively. How many strategy profiles does it have?

8.[2p]
Common knowledge of the game means

9.[3p]
Match each term to what it names.