Learning Outcomes
• Mahasiswa akan dapat menghitung penyelesaian model permainan berbagai contoh aplikasi/kasus.
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Outline Materi:
• Konsep Dasar permainan
• Model Permainan
• Aturan model Permainan
• Equiliribium & Strategy.
• Contoh kasus..
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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
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Prisoner’s dilemma
Possible strategies for Mulloy
Possible strategies for Jones
Confess
Confess
Jones: 8 years
Mulloy: 8 years
Do not confess
Jones: 10 years
Mulloy: 2 years
Do not confess
Jones: 2 years
Mulloy: 10 years
Jones: 4 years
Mulloy: 4 years
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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
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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
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Does cheating pay?
Possible strategies for Farmer
Possible strategies for Acron
Abide by agreement
Abide by agreement
Cheat
Acron
’ s
P
: $5 million Acron
’ s
P
: -$2 million
Farmer
’ s
P
: $5 million Farmer
’ s
P
: $8 million
Cheat Acron
’ s P : $8 million Acron
’ s P : $2 million
Farmer
’ s P : -$2 million Farmer
’ s P : $2 million
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Most-favored-customer clauses
1. 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
2. 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
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Payoff Matrix before
Most-favored-customer clause
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Payoff Matrix after
Most-favored-customer clause
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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
Low price
Gelhart
’ s
P
: $2 million
LIV
’ s
P
: $3 million
Gelhart
’ s
P
: $3 million
LIV
’ s
P
: -$1 million
High price
Gelhart
’ s
P
: $7 million
LIV
’ s
P
: $11 million
Gelhart
’ s
P
: $11 million
LIV
’ s
P
: $8 million
Gelhart will lose money by retaliating. Maybe reputation of being “reckless”
(regardless of costs) could help.
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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
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Deterrence of entry I
Salem has first move
Possible strategies for Lotus
Possible strategies for
Salem
Enter Do not enter
Resist entry
Lotus’s P
: $3 million
Salem’s P
: $6 million
Lotus’s P
: $13 million
Salem’s P
: $9million
Do not resist entry
Lotus’s P
: $4 million
Salem’s P
: $12 million
Lotus’s P
: $13 million
Salem’s P
: $9 million
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Deterrence of entry II
Lotus makes credible threat to resist: excess capacity
Possible strategies for Lotus
Possible strategies for
Salem
Enter Do not enter
Resist entry
Lotus’s P
: $3 million
Salem’s P
: $6 million
Lotus’s P
: $11 million
Salem’s P
: $9million
Do not resist entry
Lotus’s P
: $2 million
Salem’s P
: $12 million
Lotus’s P
: $11 million
Salem’s P
: $9 million
Excess capacity decreases Lotus’ profits in 3 out of 4 cases
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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
1. Signal a commitment to defend position in diapers through public statements, comments to retailers, etc.
2. File a patent suit
Cost to P and G
None
Cost to entrant
Raises expected cost of entry by increasing probability and extent of retaliation
3. Announce planned capacity expansion
4. Announce a new generation of diapers to be introduced in future.
Legal fees Incurs legal fees plus probability that P and G wins the suit with subsequent cost to the competitor
None Raises expected risk of price cutting and the probability of
P and G’s retaliation to entry.
None Raises expected cost of entry by forcing entrant bear possible product development and changeover costs contingent on the ultimate configuration of the new generation
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Decision tree
Expand
HP Compaq = $50
HP = $50
Expand
Don’t expand
Compaq = $150
HP = $60
Compaq
Expand
Compaq = $60
HP = $120
Don’t expand
HP
Don’t expand
Compaq = $80
HP = $80
Compaq acts first: but resolve the tree from right to left!
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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
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