Learning Outcomes
• Mahasiswa akan dapat menghitung
penyelesaian model permainan berbagai
contoh aplikasi/kasus.
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Outline Materi:
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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
Do not confess
Confess
Jones: 8 years
Mulloy: 8 years
Jones: 2 years
Mulloy: 10 years
Do not
confess
Jones: 10 years
Mulloy: 2 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
Farmer’s P: $5 million
Cheat
Acron’s P: -$2 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
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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
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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”
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(regardless of costs) could help.
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
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
None
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.
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
HP
Expand
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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