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

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

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

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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

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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

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6 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 One-shot games vs. Repeated games I

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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

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

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9 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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10 Payoff Matrix before Most-favored-customer clause

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11 Payoff Matrix after Most-favored-customer clause

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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 : $2 millionGelhart ’ s : $3 million LIV ’ s : $3 million LIV ’ s : -$1 million Gelhart ’ s : $7 millionGelhart ’ s : $11 million LIV ’ s : $11 million LIV ’ s : $8 million Gelhart will lose money by retaliating. Maybe reputation of being “reckless” (regardless of costs) could help.

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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

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

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

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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. TacticCost to P and G Cost to entrant 1. Signal a commitment to defend position in diapers through public statements, comments to retailers, etc. NoneRaises expected cost of entry by increasing probability and extent of retaliation 2. File a patent suitLegal feesIncurs legal fees plus probability that P and G wins the suit with subsequent cost to the competitor 3. Announce planned capacity expansion NoneRaises 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. NoneRaises 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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17 Decision tree Compaq Compaq = $50 HP = $50 HP Don’t expand Expand Don’t expand Compaq = $150 HP = $60 Compaq = $60 HP = $120 Compaq = $80 HP = $80 Compaq acts first: but resolve the tree from right to left!

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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

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