Econ 332, Economic Games and Strategy
Fall 2014, Exam #1
Dr. Stonebraker
Name ______________________________
1. (3%) Honda is considering a 10% price cut for its automobiles. Is this a game or a decision? Why?
2. (11%) Players A and B take turns choosing a number from 1 through 4 and keep a running,
cumulative total of their choices. The player whose number takes this running, cumulative total
exactly to 19 wins the game. Does the advantage go to the first mover or the second mover? Clearly
describe his/her optimal strategy and explain.
3. (17%) Three retail firms (Frieda's, Big Giant, and Titan) must decide whether to locate in an urban
(U) or rural (R) mall. Frieda's will choose its location first, then Big Giant, then Titan. Using the
game tree below (Frieda's payoffs are listed first, Big Giant's second, and Titan's third), determine the
equilibrium outcome and explain.
Payoffs
6, 4, 10
10, 10, 4
4, 6, 8
6, 8, 6
3, 10, 10
8, 5, 8
10, 9, 6
9, 7, 9
4. (24%) Each of two students (Elsa Econ and Polly Sigh) must decide how much effort to put into a
joint project. Each has three choices: low effort (L), medium effort (M) or high effort (H). Their
payoffs are listed in the table below. (Elsa’s payoff is listed first and Polly’s second).
Polly
Elsa
L
M
H
L
1, 1
2, 2
8, 3
M
2, 2
3, 4
5, 5
H
3, 7
4, 6
6, 4
a. Does either student initially have a dominant strategy? Explain why or why not.
b. Does either student initially have a dominated strategy? Explain why or why not.
c. Are there any Nash equilibrium sets of strategies? Explain why or why not.
5. (8%) The NCAA is designed to solve several prisoners’ dilemma games. How? Explain any one of
these.
6. (10%) Insert payoffs into the blank table below that are consistent with a Chicken game between
Verizon and T-Mobile. Are there any Nash equilibriums in your game? Explain.
Verizon
V1
T-Mobile
V2
T1
T2
7. (17%) An accountant has been thrown into a large pit with four hungry lionesses, each of whom is
well versed in game theory. Each lion is chained along a row with Lion #1 being the closest to the
accountant. Each lioness only can reach the players immediately adjacent.
The game begins by Lioness #1 deciding whether or not to eat the accountant. If she eats the
accountant she will be too fat to protect herself from Lioness #2 who then decides whether or not to
eat Lioness #1. If Lioness #1 does not eat the accountant, Lioness #2 will not attack her because any
ensuing fight between two hungry lionesses would kill both. If Lioness #2 does eat Lioness #1, she
will be too fat to defend herself from Lioness #3 who then decides whether or not to eat Lioness #2.
If Lioness #3 does eat Lioness #2, she will be too fat to defend herself from Lioness #4 who then
decides whether or not to eat Lioness #3.
Each lioness gets a payoff of 4 if she gets to eat and is not eaten, 3 if she does not eat but also is not
eaten, 2 if she gets to eat but then is eaten, and 1 if she goes hungry and still gets eaten.
a.
b.
Draw the game tree for this four-player game.
Describe the rollback equilibrium. Does anyone get eaten? Who? Explain why.
8. (10%) Both Klingon and Bajoran families prefer to live in an integrated neighborhood of rented
homes. The rents they are willing to pay for living in a four-home neighborhood depend upon the
mix of other families as given below:
Number of Klingon families
0
1
2
3
4
Rent Klingons will pay
--350
440
480
300
Rent Bajorans will pay
370
470
500
380
---
Each home is handled by a different real estate agent and each agent is trying to maximize the rent
he/she can get. What will happen? Why? Explain clearly.