ch06_solutions_S11 correx

# ch06_solutions_S11 correx - Solutions to Chapter 6...

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Solutions to Chapter 6 Exercises SOLVED EXERCISES S1. Second-mover advantage. In a sequential game of tennis, the second mover will be able to respond best to the first mover’s chosen action. Put another way, the second mover will be able to exploit the information she learns from the first mover’s action. However, since there is no Nash equilibrium in pure strategies, no outcome is the result of the players’ mutually best responding. The outcome reached will not be one that first mover would prefer, given the action of the second mover. S2. The strategic form, with best responses underlined, is shown below. 2 L R 1 U 2 , 4 4 , 1 D 3 , 3 1 , 2 There is a unique Nash equilibrium: (D, L) with payoff (3, 3). It is also the unique subgame- perfect equilibrium. S3. The strategic form is shown below.1 Boeing If in, then Peace If in, then War Airbus In \$300m, \$300m –\$100m, –\$100m Out 0, \$1b 0, \$1b There are two Nash equilibria: (In; If In, then Peace) and (Out; If In, then War). Only the first of these, (In; If In, then Peace), is subgame perfect. The outcome (Out; If In, then War) is a Nash equilibrium but is not subgame perfect; this equilibrium hinges on Airbus’s belief that Boeing will start a price war on Solutions to Chapter 6 Exercises 1 of 14

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Airbus’s entry into the market. However, Boeing lowers its own payoff by starting such a price war. Therefore threat to do so is not credible. S4. (a) The strategic form is: Tinman if N, then t if N, then b Scarecrow N 0, 2 2, 1 S 1, 0 1, 0 (b) The only Nash equilibrium is (S; if N, then t) with payoffs of (1, 0). S5. (a) The strategic form is as follows. The initials of the strategies indicate which action each player would take at his first, second, and third nodes, respectively. Tinman nnn nns nsn nss snn sns ssn sss Scarecrow NNN 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 NNS 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 NSN 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 NSS 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 SNN 2 , 3 2 , 3 2 , 3 2 , 3 5 , 4 5 , 4 5 , 4 5 , 4 SNS 2 , 3 2 , 3 2 , 3 2 , 3 5 , 4 5 , 4 5 , 4 5 , 4 SSN 4 , 5 4 , 5 3 , 2 3 , 2 5 , 4 5 , 4 5 , 4 5 , 4 SSS 1 , 0 2 , 2 3 , 2 3 , 2 5 , 4 5 , 4 5 , 4 5 , 4 Solutions to Chapter 6 Exercises 2 of 14
Pure-strategy Nash equilibria are indicated by double borders. The unique subgame-perfect Nash equilibrium is (SSN, nns), with payoffs of (4, 5). (b) The remaining Nash equilibria are not subgame perfect because a player cannot credibly threaten to make a move that will give himself a lower payoff than he would otherwise receive. The Tinman would not play strategy nnn at his third node because 0 < 1. Similarly, the twelve equilibria that arise when the Tinman plays S on his first node are not subgame perfect, because if he plays N at that node he can expect the higher payoff of 5. S6. (a) The strategic form is as follows. The initials of the Scarecrow’s strategies indicate which action he would take at his first, second, and third nodes, respectively.

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ch06_solutions_S11 correx - Solutions to Chapter 6...

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