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Sequential Games Game Theory 3

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The Advantage of Moving First Firm 2 CrispySweet Firm 1Crispy-5, -510, 20 Sweet20, 10-5, -5

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Threats, Credibility, Commitments In the product choice game, an empty threat to produce the sweet cereal has no credibility Suppose firm 1 says it will choose “sweet” If firm 2 introduces “sweet” first, firm 1 will choose “crispy” Threat of “sweet” lacks credibility If firm 1 can make a commitment to “sweet”, it’s threat is credible. Undertake an advertising campaign for “sweet” prior to intro Construct “sweet” production facility or purchase equipment Purchase futures contract for sugar delivery Choose a production technology that favors “sweet”

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Technology Choice A firm can choose between two technologies with costs C 1 = 32 + 16Q or C 2 = 220 + 4Q Demand is P = 40 – Q The firm is currently a monopolist, but faces possible entry by a firm using technology #1 If entry occurs, Cournot competition ensues Can the monopolist deter entry by choice of technology? Is it worthwhile for the monopolist to deter entry by choosing the appropriate technology?

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Calculate Monopoly Profits C 1 monopoly: C 1 = 32 + 16Q P= 40 – Q Set MR = MC or 16 = 40 – 2Q => Q = 12 P = 40 – 12 = 28 π 1 = 28(12) – 32 – 16(12) = 12(12) – 32 = 144 – 32 = 112 C 2 monopoly: C 2 = 220 + 4Q P = 40 – Q Set MR = MC or 4 = 40 – 2Q => Q = 18 P = 40 – 18 = 22 π 2 = 22(18) – 220 – 4(18) = 18(18) – 220 = 324-220 = 104 Now calculate Cournot outcomes after entry for both technology choices by firm 1

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Symmetric Cournot Both firms face C 1 = 32 + 16Q and P = 40 – (Q 1 + Q 2 ) π 1 = P 1 Q 1 – C 1 = Q 1 [40 – (Q 1 + Q 2 )] – 32 – 16Q 1 = 24Q 1 – Q 1 2 - Q 1 Q 2 – 32 ∆ π /∆Q 1 = 24 - 2Q 1 - Q 2 = 0 Reaction curves: Q 1 = 12 – ½Q 2 ; Q 2 = 12 – ½Q 1. Q 1 = 12 – ½(12 – ½Q 1 ) = 6 + ¼ Q 1 ¾ Q 1 = 6 Q 1 = 8 = Q 2 P = 40 – 16 = 24 π 1 = π 2 = 24(8) – 32 - 16(8) = 8(8) – 32 = 64 – 32 = 32

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Asymmetric Cournot Firm 1: C 2 = 220 + 4Q 1 ; Firm 2: C 1 = 32 + 16Q 2 Find Q 1 and Q 2 π 1 = Q 1 [40 – (Q 1 + Q 2 )] – 220 – 4Q 1 π 1 = 36Q 1 - Q 1 2 - Q 1 Q 2 – 220 ∆ π 1 /∆Q 1 = 36 – 2Q 1 - Q 2 = 0 Reaction curves: Q 1 = 18 – ½Q 2 ; Q 2 = 12 – ½Q 1 Q 1 = 18 – ½(12 – ½Q 1 ) = 12 + ¼ Q 1 Q 1 = 16 Q 2 = 12 – ½Q 1 = 12 – ½(16) = 12 – 8 = 4 P = 40 – (Q 1 + Q 2 ) = 40 – 20 = 20 π 1 = 20(16) – 220 – 4(16) = 256 – 220 = 36 π 2 = 20(4) – 32 - 16(4) = 4(4) – 32 = 16 – 32 = -16

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Payoff Table Firm 2 EnterStay Out Firm 1 Tech # 1 Symmetric Cournot 32, 32 Monopoly #1 112, 0 Tech #2 Asymmetric Cournot 36, -16 Monopoly #2 104, 0

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