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Chapter 10

Chapter 10 answers

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Department
Economics
Course
Economics 2163A/B
Professor
Prof
Semester
Winter

Description
Chapter 10: Answers to Questions and Problems 1. a. Player 1’s dominant strategy is B. Player 2 does not have a dominant strategy. b. Player 1’s secure strategy is B. Player 2’s secure strategy is E. c. (B, E). 2. a. Player 2 Strategy A B Player 1 A $500, $500 $0, $650 B $650, $0 $100, $100 b. B is dominant for each player. c. (B, B). d. Joint payoffs from (A, A) > joint payoffs from (A, B) = joint payoffs from (B, A) > joint payoffs from (B, B). e. No; each firm’s dominant strategy is B. Therefore, since this is a one-shot game, each player would have an incentive to cheat on any collusive arrangement. 3. a. Player 1’s optimal strategy is B. Player 1 does not have a dominant strategy. However, by putting herself in her rival’s shoes, Player 1 should anticipate that Player 2 will choose D (since D is Player 2’s dominant strategy). Player 1’s best response to D is B. b. Player 1’s equilibrium payoff is 5. 4. a. (A, C). b. No. c. If firms adopt the trigger strategies outlined in the text, higher payoffs can be π πhea− Coop 1 Cheat Coop N achieved if Coop N ≤ . Here, π = 60, π = 50, π = 10, and the π π − i π πhea− −Coop 60 50 1 11 interest rate is i = .05. SinceCoop N == = 0.25 < == 20 ππ − − 50 10 4 i .05 each firm can indeed earn a payoff of 50 via the trigger strategies. d. Yes. Managerial Economics and1 Business Strategy, 5e Page 5. a. x > 2. b. x < 2. c. x < 2. 6. a. See the accompanying figure. ($0, $15) Right 1 Right ($10, $10) Left 2 Left (-$10, $8) b. ($0, $15) and ($10, $10). c. ($10, $10) is the only subgame perfect equilibrium; the only reason ($0, $15) is a Nash equilibrium is because Player 2 threatens to play left if 1 plays left. This threat isn’t credible. 7. a. Player 1 has two feasible strategies: A or B. Player 2 has four feasible strategies: (1) W if A and Y if B; (2) X if A and Y ifB; (3) W if A and Z if B; (4) X if A and Z if B. b. (60, 120) and (100, 150). c. (100, 150). 8. a. There are two Nash equilibria: (5, 5) and (20, 20). The (5, 5) equilibrium would seem most likely since the other equilibrium entails considerable risk if the players don’t coordinate on the same equilibrium. b. “B”. This would signal to player 2 that player 1 is going to use strategy B, and therefore permit the players to coordinate on the (20, 20) equilibrium. c. Player 2 would choose Y and player 1 would follow by choosing B. This is the subgame perfect equilibrium. Page 2 Michael R. Baye 9. The normal form game looks like this: Kmart Strategy Sale Price Regular Price Target Sale Price $1, 1 $5, $3 Regular Price $3, $5 $3, $3 Notice that there are two Nash equilibria: (Sale, Regular) and (Regular, Sale) with profits of ($5, 3) and ($3, $5), respectively. Thus, there is not a clear-cut pricing strategy for either firm. One mechanism that might solve this problem is to advertise your sales on alternate weeks. Another mechanism might be to guarantee “everyday low prices” (so that you effectively commit to always charge the sale price). In this case, your rival’s best response would be to charge the regular price and your firm would earn profits of $5 million. 10. The normal form game looks like this: Ford StrateAyiAairsogs GM Airbags $1.5, 1.5 $2,-$1 No Airbags -$1, $2 $0.5, $0.5 The dominant strategy, in this case, would be to offer airbags. 11. The extensive form game looks like this: ($200, $300) Not Introduce P Price War ($100, $100) Introduce C Acquiesce ($227, $275) Notice that Coca-Cola’s best response if Pepsi introduces is to acquiesce to earn $275 million rather than to start a price war and earn $100. Thus, while Coca-Cola might threaten to start a price war in an attempt to keep you out of the market, this threat isn’t credible; your best option is to introduce. Managerial Economics and3 Business Strategy, 5e Page 12. The savings from letting the union use its own pen and ink to craft the document are most likely small compared to the advantage you would gain by making a take-it-or- leave-it offer. 13. Since you know for certain that the game will end in 1 month, your optimal strategy in the finitely repeated pricing game with a known endpoint is to reduce price (defect) from the implicit collusive agreement between you and your rival. 14. The normal form of this game looks as follows: Rival Strategy: Price Low
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