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SolutionSolution1. 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. CoyoteAnvilDynamiteRoadrunnerBeep6 , 24 , 5Run7 , 36 , 8b. BartPoutWhineMaggieLay Finger on Butterfinger6 , 811 , 3Ignore Butterfinger2 , 69 , 5c. MarthaRedWhiteJuliaSteak5 , 28 , 4Chicken6 , 17 , 32. 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.DuvallStopDropRollEarlHammer4 , 149 , 65 , 3Anvil8 , 26 , 121 , 7Stirrup11 , 516 , 39 , 8Game Theory12Goolsbee1e_Solutions_Manual_Ch12.indd 171Goolsbee1e_Solutions_Manual_Ch12.indd 17111/15/12 3:09 PM11/15/12 3:09 PM
172Part 3 Markets and PricesSolution3. For each of the following games, use dominance to find the Nash equilibrium. Each game contains only one Nash equilibrium.a. MacBethCleanSpotListen to WifeMacDuffSlay King10 , 28 , 4Roll Head6 , 44 , 5b. FerrisTwistShoutElvisBump4 , 86 , 6Grind2 , 44 , 3c. EagleTake ItEasyTake It tothe LimitMatthewGet UnderTable5 , 33 , 2Stand Up3 , 514 , 43. 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. FredOperaBowlingWilmaOpera5 , 20 , 0Bowling0 , 02 , 5b. ChuckStraightSwerveRenStraight0 , 03 , 1Swerve1 , 32 , 2Goolsbee1e_Solutions_Manual_Ch12.indd 172Goolsbee1e_Solutions_Manual_Ch12.indd 17211/15/12 3:09 PM11/15/12 3:09 PM
Game TheoryChapter 12 173SolutionSolutionSolution4. 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