Using Game Theory to Model Non-Cooperative Oligopoly

Using Game Theory

to Model Non-Cooperative Oligopoly

High Output Low Output

High Output

Firm 1

Low Output

Firm 2

$57, 57 $54, 72

$72, 54 $65, 65

Payoff Matrix for High Output/Low Output Game

Representation of HO/LO Game

Firm 2

LO

HO HO

LO

HO

LO

$57

$54

$72

$65

Payoff to firm 1

Dominant strategy for firm 1: produce High Output

Dominant strategy for firm 2: produce High Output

Market outcome: firms 1 and 2 choose HO → joint payoff= $114

HO LO

HO

Firm 1

LO

Firm 2 $57, 57 $54, 72

$72, 54 $65, 65Firm 1

Representation of HO/LO Game

No collusion Both firms 1 and 2 choose HO → joint payoff = $114

HO LO

HO

Firm 1

LO

Firm 2

$57, 57 $54, 72

$72, 54 $65, 65

With collusion Both firms 1 and 2 choose LO→ joint payoff = $130

5,5 10, 0

2,2 0, 10

Payoff Matrix for Prisoners’ Dilemma

Prisoner 2

Talk Don’t talk

Talk

Don’t Talk

Prisoner 1

Representation of Prisoner’s Game

Prisoner 2 Don’t talk

Talk

Talk

Don’t talk

Talk

Don’t talk

5 years

10 years

0 years

2 years

Payoff for prisoner 1

Dominant strategy for prisoner 1: Talk

5, 5 10, 0

2, 2 0, 10

Prisoner 2

Talk Don’t talk

Talk

Don’tTalk

Prisoner 1

Dominant strategy for prisoner 2: Talk

Market outcome: both prisoners choose Talk→ joint payoff = 10 yrs.

Representation of Prisoner’s Game

5, 5 10, 0

2, 2 0, 10

Prisoner 2

Talk Don’t talk

Talk

Don’tTalk

Prisoner 1

No collusionBoth prisoners choose Talk→ joint payoff = 10 yrs.

With collusionBoth prisoners choose Don’t Talk→ joint payoff = 4 yrs.

Advertise Don’t advertise

Advertise

Firm A

Don’t Advertise

Firm B

$10, 5 $6, 8

$15, 0 $20, 2

Payoff Matrix for Advertise/Don’t Advertise Game

Representation of Advertising Game

Firm B DA

A A

DA

A

DA

$10

$6

$15

$20

Payoff to firm A

Dominant strategy for firm A: none

Advertise Don’t advertise

Advertise

Firm A

Don’t Advertise

Firm B $10, 5 $6, 8

$15, 0 $20, 2

Representation of Advertising Game

Firm A

DA

A A

DA

A

DA

$5

$0

$8

$2

Payoff to firm B

Advertise Don’t advertise

Advertise

Firm A

Don’t Advertise

Firm B $10, 5 $6, 8

$15, 0 $20, 2

Dominant strategy for firm B: advertise

If Firm A realizes this, best strategy for firm A: advertiseMarket outcome: A & B advertise→ joint payoff = $15

Firm Mover (Stakelberg) Games: Should a Monopolist Pursue This Entry Deterrent Strategy?

• Monopolist’s profit w/o entry = $100 million

• If Entry: market becomes a duopoly with total profit $80 million: $40 million each

• Monopolist considering an entry-deterrent strategy which raises costs (both the monopolist’s and the entrant’s) by $50 million.

Raise Costs

Don’t raise costs

Enters

Monopolist

Does not enter

Entrant

$-10, -10 $40, 40

$50, 0 $100, 0

Payoff Matrix for Entry-Deterrent Strategy Game

MonopolistDon’t raise

RaiseEnters

Does not enter

Enters

Does not enter

-$10,-$10

$50, $0

$40, $40

$100, $0

Representation of Entry-Deterrent Game

Raise Costs Don’t raise costs

Enters

Monopolist

Does not

enter

Entrant

$-10,-10 $40, 40

$50, 0 $100, 0

Best strategy for monopolist: Raise costs → entrant does not enter and mon. profit = $50

Entrant Payoffs