Econ 332, Economic Games and Strategy
Fall 2014, Exam #2
Dr. Stonebraker
Name ______________________________
Remember: if Y = a + bX + cX2, then Y is maximized when X = - (b/2c)
1. (5%) Economists say that risk-averse behavior results from diminishing marginal utility of money. Why?
Clearly explain the logic.
2. (15%) Suppose that Barack and Vladimir play the simultaneous game with payoffs as listed below
(Barack’s payoff is listed first and Vladimir’s is listed second).
Vladimir
Barack
V1
V2
B1
12, 10
8, 8
B2
5, 20
18, 13
a. Identify any and all pure strategy Nash equilibriums.
b. Suppose the game becomes sequential with Vladimir moving first. Show the game in extensive form
and identify the rollback equilibrium.
3. (19%) Two firms (Econ Elites and Nobel Noggins) sell framed portraits of Nobel Prize winning
economists on Scholar’s Walk. The demand for each depends both upon its own price and that of the
other. They estimate the following functions (the E and N subscripts represent values for Econ Elites
and Nobel Noggins respectively):
QE = 40 - 2 PE + PN
and
QN = 28 – PN + PE
The average cost of making a framed photo is a constant $10 for Econ Elites and $12 for Nobel Noggins
(it provides higher quality frames).
a. Calculate the profit functions for each firm.
b. Calculate the best-response or reaction function for each firm. Show your work.
c. Calculate the Nash equilibrium prices for each firm.
4.
(14%) Each of two candy firms, Tyler's Toffee and Derek's Delights, has three possible strategies with
payoffs listed in the table below. (Tyler's payoff is listed first and Derek's second). Using this matrix
below:
Derek’s Delights
D1
Tyler's Toffee
D2
D3
T1
30, 15
24, 40
16, 30
T2
14, 38
30, 20
28, 33
T3
15, 22
28, 17
24, 26
a.
Explain how to find outcomes that are rationalizable.
b.
Find all rationalizable outcomes in the table above.
6.
(16%) Vincent and Nikki must choose whether or not to make a campaign visit to Rock Hill. Vincent
must choose first and Nikki second. The payoffs of this sequential game are listed below:
visit
-3, -3
Nikki
visit
not visit
6, -5
Vincent
visit
not visit
-4, 3
Nikki
not visit
2, 4
a. Show all possible strategies of this game in strategic or normal form.
b. Identify any and all pure strategy Nash equilibriums and explain.
c. Which, if any of these equilibriums are subgame perfect? Explain clearly.
6.
(17%) Stonebraker is serving against Raphael Nadal for the Wimbledon Tennis Championship and
must decide whether to serve to Nadal’s forehand or backhand. Nadal must anticipate what Stonebraker
will do. Their chances of success are listed in the table below (Stonebraker's chance of success is listed
first and Nadal’s is listed second).
Let p= probability that Stonebraker will serve to Nadal’s forehand and q = probability that Nadal will
expect a serve to his forehand.
Nadal
Expect forehand
Expect backhand
Forehand
Stonebraker
Backhand
20, 80
40, 60
30, 70
10, 90
a. Calculate the q-mix payoffs and show Stonebraker’s expected success for serving to both Nadal’s
forehand and backhand at different q’s on the graph below. Label everything clearly.
b. Calculate Nadal’s optimal q and Stonebraker’s expected success. Show your work.
Stonebraker’s expected success
Nadal’s q choice
7. (14%) Suppose that Nathan’s and Hebrew National each have two strategies with the payoffs listed
below. Let p = the probability of Hebrew National playing H1 and q = the probability of Nathan’s
playing N1.
Nathan’s
N1
N2
H1
4, 4
0, 1
H2
1, 0
2, 2
Hebrew National
Graph Nathan’s best response curve on the diagram below. Show your work.
p
q