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Using Game Theory to Model Non-Cooperative Oligopoly. $57, 57. $54, 72. $72, 54. $65, 65. Payoff Matrix for High Output/Low Output Game. Firm 1. High Output. Low Output. High Output. Firm 2. Low Output. $57, 57. $54, 72. $72, 54. $65, 65. - PowerPoint PPT Presentation
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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