Presentation on theme: "Pertemuan 12: Model Permainan (OFC)"— Presentation transcript:
1Pertemuan 12: Model Permainan (OFC) Mata kuliah : K0194-Pemodelan Matematika Terapan@2005, vers 01.Pertemuan 12: Model Permainan (OFC)
2Learning OutcomesMahasiswa akan dapat menghitung penyelesaian model permainan berbagai contoh aplikasi/kasus.
3Outline Materi:Konsep Dasar permainanModel PermainanAturan model PermainanEquiliribium & Strategy.Contoh kasus..
4Finding 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
5Prisoner’s dilemma Possible strategies for Mulloy Possible strategies for JonesConfessDo not confessJones: 8 years Jones: 2 yearsMulloy: 8 years Mulloy: 10 yearsJones: 10 years Jones: 4 yearsMulloy: 2 years Mulloy: 4 yearsConfessDo not confess
6One-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 priceCooperation 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 oftenBenefits of cooperation are higher if agents can interact more oftenRepeated game: gains from cooperation are much higher
7One-shot vs. Repeated games II Suppose game goes on for several periodsIf 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 problemDoes it work also, if there are only 10 periods?Use backward induction (i.e. look at last period!)End-game problem
8Does cheating pay? Possible strategies for Farmer Possible strategies for AcronAbide by agreementCheatAcron’s P: $5 million Acron’s P: -$2 millionFarmer’s P: $5 million Farmer’s P: $8 millionAcron’s P: $8 million Acron’s P: $2 millionFarmer’s P: -$2 million Farmer’s P: $2 millionAbide by agreementCheat
9Most-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 reductionOr: you get a rebate, if you see the product cheaper somewhere else. ==> BestpreisgarantieLooks 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
10Payoff Matrix before Most-favored-customer clause
11Payoff Matrix after Most-favored-customer clause
12Non-credible threats Assume: Gelhart wants to deter price cut by rival by a commitment of retaliationPossible strategies for LIVPossible strategies for GelhartLow priceHigh priceGelhart’s P: $2 million Gelhart’s P: $3 millionLIV’s P: $3 million LIV’s P: -$1 millionGelhart’s P: $7 million Gelhart’s P: $11 millionLIV’s P: $11 million LIV’s P: $8 millionLow priceHigh priceGelhart will lose money by retaliating. Maybe reputation of being “reckless” (regardless of costs) could help.
13Example 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
14Deterrence of entry I Salem has first move Possible strategies for SalemPossiblestrategiesfor LotusEnterDo not enterLotus’s P: $3 million Lotus’s P: $13 millionSalem’s P: $6 million Salem’s P: $9millionLotus’s P: $4 million Lotus’s P: $13 millionSalem’s P: $12 million Salem’s P: $9 millionResist entryDo not resist entry
15Deterrence of entry II Lotus makes credible threat to resist: excess capacity Possible strategies for SalemPossiblestrategiesfor LotusEnterDo not enterLotus’s P: $3 million Lotus’s P: $11 millionSalem’s P: $6 million Salem’s P: $9millionLotus’s P: $2 million Lotus’s P: $11 millionSalem’s P: $12 million Salem’s P: $9 millionResist entryDo not resist entryExcess capacity decreases Lotus’ profits in 3 out of 4 cases
16Case studyIn 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 GCost to entrant1. 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 retaliation2. File a patent suitLegal feesIncurs legal fees plus probability that P and G wins the suit with subsequent cost to the competitor3. Announce planned capacity expansionRaises 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
17Decision treeExpandHPCompaq = $50 HP = $50ExpandCompaq = $150 HP = $60Don’t expandCompaqCompaq = $60 HP = $120ExpandDon’t expandCompaq = $80 HP = $80HPDon’t expandCompaq acts first: but resolve the tree from right to left!
18Other 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 betterCoordination paysChicken gameJohn and Jack race with the car against each otherSee „Rebel without a cause“ with James Dean