Goolsbee1e_Solutions_Manual_Ch12 - 12 Game Theory 1 Consider the game on the right a Who are the players in this game b What strategies are available to

Goolsbee1e_Solutions_Manual_Ch12 - 12 Game Theory 1...

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Solution Solution 1. Consider the game on the right: a. Who are the players in this game? b. What strategies are available to Duvall? c. If Earl plays Hammer and Duvall plays Roll, then what is Earl’s payoff? d. If Earl plays Stirrup and Duvall plays Drop, what is Duvall’s payoff? 1. a. The players are Duvall and Earl. b. Duvall’s strategies are Stop, Drop, and Roll. c. If Earl plays Hammer and Duvall plays Roll, Earl’s payoff is 5. d. If Earl plays Stirrup and Duval plays Drop, Duvall’s payoff is 3. 2. For each player in the following games, find the dominant strategy, if any. a. Coyote Anvil Dynamite Roadrunner Beep 6 , 2 4 , 5 Run 7 , 3 6 , 8 b. Bart Pout Whine Maggie Lay Finger on Butterfinger 6 , 8 11 , 3 Ignore Butterfinger 2 , 6 9 , 5 c. Martha Red White Julia Steak 5 , 2 8 , 4 Chicken 6 , 1 7 , 3 2. a. Roadrunner’s dominant strategy is to Run because 7 > 6 and 6 > 4, and Coyote’s dominant strategy is to Dynamite because 5 > 2 and 8 > 3. b. Maggie’s dominant strategy is to Lay Finger on Butterfinger and Bart’s dominant strategy is to Pout. c. Julia has no dominant strategy and Martha’s dominant strategy is White. Duvall Stop Drop Roll Earl Hammer 4 , 14 9 , 6 5 , 3 Anvil 8 , 2 6 , 12 1 , 7 Stirrup 11 , 5 16 , 3 9 , 8 Game Theory 12 Goolsbee1e_Solutions_Manual_Ch12.indd 171 Goolsbee1e_Solutions_Manual_Ch12.indd 171 11/15/12 3:09 PM 11/15/12 3:09 PM
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172 Part 3 Markets and Prices Solution 3. For each of the following games, use dominance to find the Nash equilibrium. Each game contains only one Nash equilibrium. a. MacBeth Clean Spot Listen to Wife MacDuff Slay King 10 , 2 8 , 4 Roll Head 6 , 4 4 , 5 b. Ferris Twist Shout Elvis Bump 4 , 8 6 , 6 Grind 2 , 4 4 , 3 c. Eagle Take It Easy Take It to the Limit Matthew Get Under Table 5 , 3 3 , 2 Stand Up 3 , 5 14 , 4 3. a. Both players have dominant strategies. MacDuff’s dominant strategy is Slay King. McBeth’s dominant strategy is Listen to Wife. Therefore, by dominance, the Nash equilibrium of this game is (8, 4) or (Slay King, Listen to Wife). b. Both players have dominant strategies. The dominant strategy for Elvis is Bump. Ferris’ dominant strategy is Twist. Therefore, by dominance, the Nash equilibrium for this game is (4, 8) or (Bump, Twist). c. Only Eagle has a dominant strategy in this game, namely Take It Easy. Given that Eagle will always play Take It Easy, the best choice for Matthew is Get Under Table. Therefore, by dominance, the Nash equilibrium in this game is (5, 3) or (Get Under Table, Take It Easy). 4. Use best-response analysis (the check method) to find the Nash equilibrium or equilibria (if any) in each of the following games. a. Fred Opera Bowling Wilma Opera 5 , 2 0 , 0 Bowling 0 , 0 2 , 5 b. Chuck Straight Swerve Ren Straight 0 , 0 3 , 1 Swerve 1 , 3 2 , 2 Goolsbee1e_Solutions_Manual_Ch12.indd 172 Goolsbee1e_Solutions_Manual_Ch12.indd 172 11/15/12 3:09 PM 11/15/12 3:09 PM
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Game Theory Chapter 12 173 Solution Solution Solution 4. a. When Wilma chooses Opera, Fred’s best response is to also choose Opera. When Wilma chooses Bowl- ing, Fred’s best response is to also choose Bowling. Similarly, when Fred chooses Opera, Wilma should also choose Opera, and when Fred chooses Bowling, so should Wilma. Therefore, there are two Nash
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