Goolsbee1e_Solutions_Manual_Ch12 - 12 Game Theory 1...

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
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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
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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