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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Game theory
• Attempts to study decision making in situations where there
is a mixture of conflict and cooperation
• A game is a competitive situation where two or more
persons pursue their own interests and no person can
dictate the outcome
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Definitions
• Rules of the game: describe how resources can be
employed
• Strategy: a complete specification of what a player will
do under each contingency in the playing of the game
• Payoff matrix: set of rewards to players depending upon
the outcome of the game
• Central oligopoly problem: whatever I do, I must know
that the other firm will react to my actions.
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Dominant strategy
• Strategy that is “best” for one player, regardless of the
strategy adopted by the other
• Simple outcome, no strategic problems arise
• Are there any incentives to change behavior?
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Dominant strategy
Possible strategies for Barkley
Possible strategies for
Allied
1
A
B
2
Allied’s P: $3 million
Barkley’s P: $4 million
Allied’s P: $2 million
Barkley’s P: $3 million
Allied’s P: $4 million
Barkley’s P: $3 million
Allied’s P: $3 million
Barkley’s P: $2 million
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No Dominant strategy for Barkley
Possible strategies for Barkley
Possible strategies for
Allied
1
A
B
2
Allied’s P: $3 million
Barkley’s P: $4 million
Allied’s P: $2 million
Barkley’s P: $3 million
Allied’s P: $4 million
Barkley’s P: $3 million
Allied’s P: $3 million
Barkley’s P: $4 million
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Nash equilibrium
• A set of strategies such that each player believes (accurately) that it
is doing the best it can given the strategy of the other player(s)
• How to find a Nash eq.: No player should have an incentive to
deviate, then the strategy is a Nash-Equilibrium
• Note: all equilibria in dominant strategies are automatically also
Nash-equilibria
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Two Nash equilibria
Possible strategies for Barkley
Possible strategies for
Allied
1
A
B
2
Allied’s P: $5 million
Barkley’s P: $5 million
Allied’s P: $0 million
Barkley’s P: $0 million
Allied’s P: $0 million
Barkley’s P: $0 million
Allied’s P: $5 million
Barkley’s P: $5 million
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Cournot-Nash Duopoly
• Some simplifying assumptions:
– 2 firms
– Same (constant) cost functions
– Know the (linear) demand function
• Taking the other‘s output as given, what output is optimal
for firm X?
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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
Cost to entrant
1. Signal a commitment to defend position in
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
3. Announce planned capacity expansion
None
Raises expected risk of price cutting and the probability of P and G’s retaliation to
4. Announce a new generation of diapers to be
None
Raises expected cost of entry by forcing entrant bear possible product development
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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