Game Theory

Question 1

What are the 8 Elements of a Game

Answer 1

Players
Actions
Order of Play
Information
Strategies
Payoffs
Outcome
Equilibrium

Question 2

What is the Equilibrium of a Game?

Answer 2

Strategy profile w/ Best Strategies for each player in a game

Question 3

What does Complete Info mean?

Answer 3

Each Player knows all payoffs for all players

Question 4

What is a Dominant Strategy?

Answer 4

Strategy where payoff for each decision are preferable to other strategy Regardless of Other Players decision

Question 5

How does Iterated Elimination of Strictly Dominated Strategies Solve games?

Answer 5

Eliminates Strategies a Rational Player would NEVER play

Question 6

What is the problem with IEoSDS?

Answer 6

Imprecise prediction about play of the Game

- i.e. If there is NO Strictly Dominated Strategy

Question 7

Define Nash Equilibrium

Answer 7

Each players Predicted Strategy must be their Best Response to Predicted Strategy of Other Players
–> No Player wants to Deviate from Predicted Strategy

Question 8

Why is NE a Stronger Solution concept than IEoSDS?

Answer 8

Strategies in NE ALWAYS survive IEoSDS

- Reverse NOT true

Question 9

What does it mean if there are No Unique Solutions?

Answer 9

There are Multiple NE

Question 10

What is the Cournot Duopoly Model?

Answer 10

2 Firms- Choose Output Quantity Simultaneously

Question 11

What is NE for Cournot Model?

Answer 11

NE => q1* = q2*
If a firm picks higher output- Lower price- Loss Making
If a firm picks lower Output- Higher price- Other firm steals Market share

Question 12

What happens to Equilibrium in Cournot?

Answer 12

Firms have Same Output
Same Market Price
Same Profits
Aggregate Output = 2 x qi

Question 13

What is Bertrand Duopoly Model?

Answer 13

Firms choose Prices instead of Quantities- still use NE

Question 14

How do firms choose Price in Bertrand?

Answer 14

Anticipate Price set by Other firm

- Each price must be Profit max. choice- given other firm’s decision

Question 15

What is NE of Bertrand Model?

Answer 15

p = MC

Question 16

Why is NE of Bertrand where p = MC?

Answer 16

p < MC : Make Loss on each unit sold- Increase Profit by Decreasing Output - (Increase MR)
p > MC : Either firm can undercut other by arbitrarily small amount, ⍷ > 0 - charge p - ⍷ - Steal all customers
Only Eq. is Competitive Eq. - Zero Profit (Bertrand Paradox)

Question 17

How do you find NE for Differentiated Products?

Answer 17

Find Firm i’s Best Response to Firm j’s Eq. Price, pj*

Sub. one BR function into other firms BR function

Question 18

What are the Slopes of BR functions in Cournot?

Answer 18

Negative Slope - ∂qi / ∂qj = –1/2 < 0
If one firm Increases Output- Optimal for other firm to Decrease Output
-Strategic Substitutes

Question 19

What are the Slopes of BR functions in Bertrand?

Answer 19

Positive Slope
∂pi / ∂pj = b/2 > 0
If one Firm Increases Price- Optimal for other to Increase Price
-Strategic Complements