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Unformatted text preview: 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. 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 oneshot 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 achieved if 1 . Cheat Coop Coop N i π π π π ≤ Here, π Cheat = 60, π Coop = 50, π N = 10 , and the interest rate is i = .05 . Since 60 50 1 0.25 50 10 4 Cheat Coop Coop N π π π π = = = < 1 1 20 .05 i = = each firm can indeed earn a payoff of 50 via the trigger strategies. d. Yes. Managerial Economics and Business Strategy, 7e Page 1 Player 1 Player 2 Strategy A B A $500, $500 $0, $650 B $650, $0 $100, $100 5. a. x > 2. b. x < 2. c. x < 2. 6. a. See the accompanying figure. ($0, $15) Right Right ($10, $10) Left 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 if B; (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 2 9....
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This note was uploaded on 11/20/2010 for the course ECONOMICS 331 taught by Professor Mj during the Fall '10 term at University of Alberta.
 Fall '10
 MJ
 Game Theory

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