1. Pertemuan 12: Model Permainan (OFC)
Mata kuliah : K0194-Pemodelan Matematika Terapan
@2005, vers 01.
Pertemuan 12: Model Permainan (OFC)

2. Learning Outcomes
Mahasiswa akan dapat menghitung penyelesaian model permainan berbagai contoh aplikasi/kasus.

3. Outline Materi:
Konsep Dasar permainan
Model Permainan
Aturan model Permainan
Equiliribium & Strategy.
Contoh kasus..

4. Finding the reaction curves
Reaction curve: given the output of X, what output of Y is optimal?
Of course, whatever Y does, will produce further reactions, i.e. X is not constant in general.
Equilibrium only when both firms „sit“ on their reaction curves: no surprises and no incentive to alter the behavior

5. Prisoner’s dilemma Possible strategies for Mulloy
Possible strategies for Jones
Confess
Do not confess
Jones: 8 years Jones: 2 years
Mulloy: 8 years Mulloy: 10 years
Jones: 10 years Jones: 4 years
Mulloy: 2 years Mulloy: 4 years
Confess
Do not confess

6. One-shot games vs. Repeated games I
Assume a cartel game: 2 firms want to set the price high to maximize profits in the cartel.
But each firm has an incentive to cheat and reduce its price
Cooperation is very difficult to establish if players interact only once (one-shot game)
Only Nash-equilibrium is low/low.
Why is it that you do observe cartels (cooperation) in real life???
Players in real life do not interact only once, they interact more often
Benefits of cooperation are higher if agents can interact more often
Repeated game: gains from cooperation are much higher

7. One-shot vs. Repeated games II
Suppose game goes on for several periods
If one player cheats, the other can punish him later (set also a low price)
Tit-for-tat strategy: each player should do, what the other did in the previous round: solves cooperation problem
Does it work also, if there are only 10 periods?
Use backward induction (i.e. look at last period!)
End-game problem

8. Does cheating pay? Possible strategies for Farmer
Possible strategies for Acron
Abide by agreement
Cheat
Acron’s P: $5 million Acron’s P: -$2 million
Farmer’s P: $5 million Farmer’s P: $8 million
Acron’s P: $8 million Acron’s P: $2 million
Farmer’s P: -$2 million Farmer’s P: $2 million
Abide by agreement
Cheat

9. Most-favored-customer clauses
If the firm reduces its price subsequent to a purchase, the early customer will get a rebate so that he or she will pay no more than those buying after the price reduction
Or: you get a rebate, if you see the product cheaper somewhere else. ==> Bestpreisgarantie
Looks like a very generous (consumer-friendly) device.
But: clever agreement to keep cartel discipline alive.
U.S. Justice Department sees such clauses as “tacit coordination” between oligopolists

10. Payoff Matrix before Most-favored-customer clause

11. Payoff Matrix after Most-favored-customer clause

12. Non-credible threats Assume: Gelhart wants to deter price cut by rival by a commitment of retaliation
Possible strategies for LIV
Possible strategies for Gelhart
Low price
High price
Gelhart’s P: $2 million Gelhart’s P: $3 million
LIV’s P: $3 million LIV’s P: -$1 million
Gelhart’s P: $7 million Gelhart’s P: $11 million
LIV’s P: $11 million LIV’s P: $8 million
Low price
High price
Gelhart will lose money by retaliating. Maybe reputation of being “reckless” (regardless of costs) could help.

13. Example for non-credible threat: NATO nuclear strategy
Mutually assured destruction: in case of a first strike by the Russians, U.S. threatens to retaliate by basically destroying the world.
But after the first strike, this strategy is not credible anymore, because payoffs for U.S. will further fall.
Remedy: construct automatic counter-attack device ==> serves as a self-binding commitment device

14. Deterrence of entry I Salem has first move
Possible strategies for Salem
Possible
strategies
for Lotus
Enter
Do not enter
Lotus’s P: $3 million Lotus’s P: $13 million
Salem’s P: $6 million Salem’s P: $9million
Lotus’s P: $4 million Lotus’s P: $13 million
Salem’s P: $12 million Salem’s P: $9 million
Resist entry
Do not resist entry

15. Deterrence of entry II Lotus makes credible threat to resist: excess capacity
Possible strategies for Salem
Possible
strategies
for Lotus
Enter
Do not enter
Lotus’s P: $3 million Lotus’s P: $11 million
Salem’s P: $6 million Salem’s P: $9million
Lotus’s P: $2 million Lotus’s P: $11 million
Salem’s P: $12 million Salem’s P: $9 million
Resist entry
Do not resist entry
Excess capacity decreases Lotus’ profits in 3 out of 4 cases

16. Case study
In the 1960s, Procter and Gamble recognized that disposable diapers could be made a mass-market product, and developed techniques to produce diapers at high speed and correspondingly low cost. The result: it dominated the market. According to Harvard’s Michael Porter, who has made a careful study of this industry, the following were some ways in which Procter and Gamble might have signalled other firms to deter entry.
Tactic
Cost to P and G
Cost to entrant
1. Signal a commitment to defend position in diapers through public statements, comments to retailers, etc.
None
Raises expected cost of entry by increasing probability and extent of retaliation
2. File a patent suit
Legal fees
Incurs legal fees plus probability that P and G wins the suit with subsequent cost to the competitor
3. Announce planned capacity expansion
Raises expected risk of price cutting and the probability of P and G’s retaliation to entry.
4. Announce a new generation of diapers to be introduced in future.
Raises expected cost of entry by forcing entrant bear possible product development and changeover costs contingent on the ultimate configuration of the new generation

17. Decision tree
Expand HP
Compaq = $50 HP = $50
Expand
Compaq = $150 HP = $60
Don’t expand
Compaq
Compaq = $60 HP = $120
Expand
Don’t expand
Compaq = $80 HP = $80 HP
Don’t expand
Compaq acts first: but resolve the tree from right to left!

18. Other fun games Battle of the sexes
Sam and Dolly would like to go out on Saturday night:
Either to Disco or to Boxing, but together would be better
Coordination pays
Chicken game
John and Jack race with the car against each other
See „Rebel without a cause“ with James Dean

19. Terima kasih,
semoga berhasil..