# Sequential Games Game Theory 3. The Advantage of Moving First Firm 2 CrispySweet Firm 1Crispy-5, -510, 20 Sweet20, 10-5, -5.

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Sequential Games Game Theory 3

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

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”

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?

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

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

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

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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