Using Game Theory to Model Non-Cooperative Oligopoly

1. Using Game Theory to Model Non-Cooperative Oligopoly

2. $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

3. $57, 57 $54, 72 $72, 54 $65, 65 Representation of HO/LO Game Firm 1 HO LO HO Firm 2 Firm 1 Payoff to firm 1 LO HO $57 HO $54 LO Firm 2 HO $72 LO LO $65 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

4. $57, 57 $54, 72 $72, 54 $65, 65 Representation of HO/LO Game Firm 1 HO LO HO Firm 2 LO No collusion Both firms 1 and 2 choose HO →joint payoff = $114 With collusion Both firms 1 and 2 choose LO→joint payoff = $130

5. 5,5 10, 0 0, 10 2,2 Payoff Matrix for Prisoners’ Dilemma Prisoner 1 Talk Don’t talk Talk Prisoner 2 Don’t Talk

6. 5, 5 10, 0 2, 2 0, 10 Representation of Prisoner’s Game Prisoner 1 Talk Don’t talk Talk Prisoner 2 Don’t Talk Payoff for prisoner 1 Talk 5 years Talk Don’t talk 10 years Prisoner 2 Talk 0 years Don’t talk Don’t talk 2 years Dominant strategy for prisoner 1: Talk Dominant strategy for prisoner 2: Talk Market outcome: both prisoners choose Talk→joint payoff = 10 yrs.

7. 5, 5 10, 0 2, 2 0, 10 Representation of Prisoner’s Game Prisoner 1 Talk Don’t talk Talk Prisoner 2 Don’t Talk No collusion Both prisoners choose Talk→joint payoff = 10 yrs. With collusion Both prisoners choose Don’t Talk→joint payoff = 4 yrs.

8. Payoff Matrix for Advertise/Don’t Advertise Game $10, 5 $6, 8 $15, 0 $20, 2 Firm A Advertise Don’t advertise Advertise Firm B Don’t Advertise

9. $10, 5 $6, 8 $20, 2 $15, 0 Firm A Representation of Advertising Game Advertise Don’t advertise Advertise Firm B Don’t Advertise Payoff to firm A A $10 A DA $6 Firm B A $15 DA DA $20 Dominant strategy for firm A: none

10. $10, 5 $6, 8 $20, 2 $15, 0 Representation of Advertising Game Firm A Advertise Don’t advertise Advertise Firm B Don’t Advertise Payoff to firm B A $5 A DA $0 Firm A A $8 DA DA $2 Dominant strategy for firm B: advertise If Firm A realizes this, best strategy for firm A: advertise Market outcome: A & B advertise→ joint payoff =$15

11. 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.

12. $-10, -10 $40, 40 $50, 0 $100, 0 Payoff Matrix for Entry-Deterrent Strategy Game Monopolist Raise Costs Don’t raise costs Enters Entrant Does not enter

13. Representation of Entry-Deterrent Game $-10,-10 $40, 40 $50, 0 $100, 0 Monopolist Raise Costs Don’t raise costs Enters Entrant Does not enter Entrant Payoffs Enters -$10,-$10 Raise Does not enter $50, $0 Monopolist Enters $40, $40 Don’t raise Does not enter $100, $0 Best strategy for monopolist: Raise costs→ entrant does not enter and mon. profit = $50