Game Theory

Question 1

The Prisoners Dilemma

Answer 1

2 individuals, X and Y.

• X and Y have been caught together committing a crime. Conclusive evidence, that X and Y are guilty of the “less serious crime”
• There is “weak” evidence that X and Y are guilty of a “more serious” crime
• How do authorities convict X and Y of the “more serious crime”?
• Authorities separate X and Y, and offer a deal. “We have enough evidence to send you to jai for 1 year. However if you confuses to the “more serious crime” and implicate your partner, you will get 3 months. Your partner gets 20 years. If you both confess, each of you get 15 years.

Question 2

Prisoners Dilemma problem

Answer 2

X

If Y confesses, I confess
If Y denies, I confess

X’s dominant strategy is CONFESS

Y

If X confesses, I confess
If X denies, I confess

Y’s dominant strategy is CONFESS

BOTH OF THEM CONFESSING IS THE NASH EQUILIBRIUM

Question 3

What happens when they both don’t have a dominant strategy?

Answer 3

See if they match

Question 4

Cooperation or Competition?

Answer 4

1. The tendency to cooperate is greater for small number of sellers than for larger numbers
2. The tendency to cooperate is greater for producers of similar products than for producers of differentiated products
3. The tendency to cooperate is greater in growing markets
4. The tendency to cooperate msg greater when entry barriers are higher
5. Tendency to cooperate is greater when the market has a dominant firm

OPEC (Canada is not in it because US, Saudi Arabia is the dominant one in the cartel)

Question 5

What are the Measures of Concentration ?

Answer 5

How much of a market is controlled by a small number of firms

1) Concentration Ratio
2) Herfindahl - Herschman Index (HHI)

Question 6

Measures of Concentration - Concentration Ratio

Answer 6

Four firm concentration ratio (CR4)

Is the percentage of the value of sales accounted for by the FOUR largest firms

Firm 1: 250
Firm 2: 200
Firm 3: 150
Firm 4: 100

Total: 700

Total Market Sales: 875

CR4 = 250 + 200 + 150 + 100 / 875
x 100

CR4 = 700 / 875 X 100 = 80%

Question 7

Measures of Concentration - Hirshman Index

Answer 7

HHI4 = (Sales 1 / Market Sales x 100) 2squared

+ (Sales 2 / Market Sales X 100) 2squared

+ (Sales 3 / Market Sales X 100) 2squared

+ (Sales 4 / Market Sales X 100) 2squared

EX.

HHI (250/875 x 100) 2squared + (200/875 x 100)2squared + (150/875 x 100)2squared + (100/875 x 100)2squared = ?

If the HHI is GREATER than 1800, the industry is considered HIGHLY CONCENTRATED

If 1000

Question 8

Definition of the industry or market

Answer 8

Several firms actually operate in several markets

ex. Proctor and gamble

Question 9

Definition of the Geographical Region

Answer 9

Ex. Concrete products (can’t rlly ship to a Toronto company wouldn’t compete with Edmonton) But for soft drinks you can target the whole country