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The University of New South Wales 
Term 3, 2021 
GSOE9210 Engineering Decisions 
sample final exam 
GSOE9210 Instructions: 
• Time allowed: 2 hours 
• Reading time: 10 minutes 
• This paper has 19 pages 
• Total number of questions: 53 (multiple choice) 
• Total marks available: 60 (not all questions are of equal value) 
• Allowed materials: UNSW approved calculator, pencil (2B), pen, ruler, 
language dictionary (paper) 
This exam is closed-book. No books, study notes, or other study ma- 
terials may be used 
• Provided materials: generalised multiple choice answer sheet, graph 
paper (1 page), working out booklet 
• Answers should be marked in pencil (2B) on the accompanying multiple 
choice answer sheet 
• The exam paper may not be retained by the candidate 
1 
Start of exam 
Questions 1 to 7 refer to the problem below. 
Recall the school fund-raiser example from lectures. There are two options 
for the fund-raising activity: a feˆte (F) or a sports day (S). The money raised 
by each activity depends on the (unpredictable) weather: on a dry day (d) 
a feˆte will make a profit of $150 and a sports day only $120; however, on a 
wet day (w) the sports day will earn $85 and the feˆte only $75. 
Suppose Alice has no information about the likelihood of whether any given 
day will be dry or wet. The fund-raiser is a once-off event; i.e., it will only 
be held once on a particular day. 
1. (1 mark) On any given day, which of the two activities (S or F) will ensure 
the greatest lower bound on profit? 
a) S only 
b) F only 
c) both S and F 
d) neither S nor F 
e) a mixture of S and F 
2. (1 mark) Suppose Alice is more concerned about limiting the maximum 
regret—she doesn’t like to miss out on opportunities. Which activity would 
Alice prefer? 
a) S only 
b) F only 
c) both S and F 
d) neither S nor F 
e) a mixture of S and F 
For the following questions assume the following: 
Suppose now that Alice works for the local branch of the Government’s ed- 
ucation department. She is in charge of twelve local schools, and is planning 
to hold a single-day fund-raiser in each school on the same day. She can hold 
different activities in different schools, if she wishes. 
2 
3. (1 mark) In how many schools should Alice hold a sports day if she wants 
to ensure the greatest minimum profit? 
a) in none of them 
b) in four of them 
c) in six of them 
d) in eight of them 
e) in all twelve of them 
4. (1 mark) In how many schools should a sports day be hosted if limiting the 
maximum regret is the main consideration? 
a) in none of them 
b) in three of them 
c) in four of them 
d) in six of them 
e) in all twelve of them 
For the following question, suppose that fund-raising events are held in one 
day of each week of every month. 
5. (1 mark) Let p = P (d) be the probability that any given day is dry. Which 
is the Bayes action for probability p = 1 
2 
? 
a) S only 
b) F only 
c) both S and F 
d) neither S nor F 
e) a mixture of S and F 
Records kept over the last ten years indicate that, on average, the number 
of dry days per month in Alice’s geographic area are as follows:1 
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 
Dry days 15 13 10 8 6 5 5 7 11 13 14 16 
1Note that Alice lives in a very wet area; perhaps a mountain valley. 
3 
6. (2 marks) Alice holds her fund-raisers every month except the one month 
in which she takes her annual holidays. If Alice is concerned with limiting 
the maximum regret, which of the options below would be the best time for 
Alice to take her holidays? 
a) Jan or Feb 
b) Feb or Sep 
c) June or July 
d) Apr or Aug 
e) Jan or Dec 
7. (1 mark) If Alice were concerned with securing the greatest minimum profit, 
in which months should she schedule her holidays? 
a) Jan or Feb 
b) Feb or Sep 
c) June or July 
d) Apr or Aug 
e) Jan or Dec 
Questions 8 to 22 refer to decision table below. 
Consider the following decision table for a problem in which the outcomes 
are measured in dollars ($). 
s1 s2 
a1 10 50 
a2 40 20 
There are two agents, A and B, who are making independent decisions on 
which of the possible actions (a1 and a2) to take—note that this is not a 
game: both agents are choosing separate decisions at different times. 
Consider agent A first. Agent A’s utility function for money is logarithmic 
(with base 2); i.e., u(x) = log2(x − a), where a ∈ R is a parameter to be 
determined. 
4 
8. (1 mark) If u(10) = 0, which alternative below best describes the utility 
function u(x)? 
a) log(x) 
b) log(x− 1) 
c) log(x + 9) 
d) log(x− 9) 
e) none of the above 
9. (1 mark) Let p = P (s1). If p = 
1 
2 
, which of the following statements is 
correct? 
a) a1 has greater expected dollar value than a2 
b) a2 has greater expected dollar value than a1 
c) both actions have the same expected dollar value 
d) a1 is dominated 
e) none of the above 
10. (2 marks) For p = 1 
2 
, which of the following statements is true? 
a) A prefers a1 to a2 
b) A prefers a2 to a1 
c) A is indifferent between the two actions 
d) A prefers neither action 
e) none of the above 
11. (1 mark) For which value(s) of p would A be indifferent between the two 
actions? 
a) p = 0 
b) 0 < p 6 1 
4 
c) 1 
4 
< p 6 1 
2 
d) 1 
2 
< p < 3 
4 
e) 3 
4 
6 p 
5 
12. (1 mark) For p = 1 
2 
, the certainty equivalent of a1 is closest to . . . 
a) $0 
b) $10 
c) $15 
d) $25 
e) $45 
13. (1 mark) For p = 1 
2 
, the certainty equivalent of a2 is closest to . . . 
a) $0 
b) $10 
c) $15 
d) $25 
e) $45 
14. (1 mark) For p = 1 
2 
, what is the approximate value of the risk premium of 
a1? 
a) $0 
b) −$10 
c) −$6 
d) $15 
e) $20 
15. (1 mark) For p = 1 
2 
, what is the approximate value of the risk premium of 
a2? 
a) $0 
b) −$10 
c) −$3 
d) $3 
e) $10 
For agent B all we know is that she is indifferent between a certain $20 and 
10% chance of $50 and 90% of $10. She is also indifferent between $40 and 
the lottery [ 6 
10 
: $50| 4 
10 
: $10]. 
Assume in the following questions that p = P (s1) = 
1 
2 
. 
6 
16. (1 mark) Which of the following statements is true? 
a) B prefers a1 to a2 
b) B prefers a2 to a1 
c) B is indifferent between the two actions 
d) B prefers neither action 
e) none of the above 
17. (2 marks) Assume that utilities for dollar values other than those given 
can be linearly interpolated. For a utility scale in the range [0, 10], which 
expression below best represents u(x) for $20 6 x 6 $40? 
a) x− 10 
b) 1 
10 
x− 1 
c) 2 
5 
x− 10 
d) 4− 4x 
e) 1 
4 
x− 4 
18. (1 mark) The certainty equivalent of a1 is closest to . . . 
a) $20 
b) $25 
c) $30 
d) $35 
e) $40 
19. (1 mark) The certainty equivalent of a2 is closest to . . . 
a) $0 
b) $10 
c) $15 
d) $25 
e) $45 
7 
20. (1 mark) What is the approximate value of the risk premium of a1? 
a) $0 
b) −$10 
c) −$6 
d) $15 
e) $20 
21. (1 mark) What is the approximate value of the risk premium of a2? 
a) $0 
b) −$10 
c) −$3 
d) $3 
e) $10 
22. (1 mark) For which value of p = P (s1) would B be indifferent between the 
two actions? 
a) 1 
10 
b) 1 
5 
c) 2 
5 
d) 3 
5 
e) 7 
10 
Questions 23 to 26 refer to the problem below. 
Two friends agree to “meet at the park”, but subsequently each realises 
that there are two identical parks (A and B) nearby. Each friend has to 
decide, independently, to which park to go to meet their friend. The game 
is modelled by the matrix below. 
A B 
A 1, 1 0, 0 
B 0, 0 1, 1 
11 
00 
8 
23. (1 mark) How many plays survive simplification by elimination of dominated 
strategies? 
a) none 
b) one 
c) two 
d) three 
e) four 
24. (1 mark) How many equilibrium points does this game have? 
a) none 
b) one 
c) two 
d) three 
e) four 
25. (1 mark) How many Pareto optimal plays are there in this game? 
a) none 
b) one 
c) two 
d) three 
e) four 
26. (1 mark) Suppose Alice believes that the probability of Bob going to park A 
is p = PB(A). Which value of p would leave Alice indifferent between going 
to either park? 
a) p = 0 
b) p = 1 
4 
c) p = 1 
3 
d) p = 1 
2 
e) for any p ∈ [0, 1] 
Questions 27 to 30 refer to problem below. 
Alice and Bob have agreed to meet for lunch. Alice prefers restaurant A 
and Bob prefers restaurant B. Unfortunately, they didn’t specify at which 
9 
restaurant they were to meet. This ‘game’ is modelled by the following game 
matrix. 
a b 
A 2, 1 0, 0 
B 0, 0 1, 2 
21 
00 
27. (1 mark) How many plays survive simplification by elimination of dominated 
strategies? 
a) none 
b) one 
c) two 
d) three 
e) four 
28. (1 mark) How many equilibrium points does this game have? 
a) none 
b) one 
c) two 
d) three 
e) four 
29. (1 mark) How many Pareto optimal plays are there in this game? 
a) none 
b) one 
c) two 
d) three 
e) four 
10 
30. (1 mark) Suppose Alice believes that the probability of Bob going to restau- 
rant A is p = PB(a). Which value of p would leave Alice indifferent between 
going to either restaurant? 
a) p = 0 
b) p = 1 
4 
c) p = 1 
3 
d) p = 1 
2 
e) for any p ∈ [0, 1] 
Questions 31 to 33 refer to the problem below. 
Alice and Bob, who are tennis partners, agreed to play this weekend. There 
are two tennis courts near them, A and B, but they didn’t specify at which 
court they would play. Court A is closer to both. This ‘game’ is modelled 
by the following game matrix. 
a b 
A 2, 2 0, 0 
B 0, 0 1, 1 
22 
00 
31. (1 mark) How many equilibrium points does this game have? 
a) none 
b) one 
c) two 
d) three 
e) four 
32. (1 mark) How many Pareto optimal plays are there in this game? 
a) none 
b) one 
c) two 
d) three 
e) four 
11 
33. (1 mark) Suppose Alice believes that the probability of Bob going to court 
A is p = PB(a). Which value of p would leave Alice indifferent between going 
to either court? 
a) p = 0 
b) p = 1 
4 
c) p = 1 
3 
d) p = 1 
2 
e) for any p ∈ [0, 1] 
Questions 34 to 36 refer to problem below. 
Alice sells magazines. She advertises her business by sending out promotional 
leaflets to her customers. She has printed three types of leaflet (A, B, or C), 
but she can only afford to send one leaflet per customer. Her market—the 
customers to which she sells her magazines—is segmented into two categories, 
s1 and s2. 
Her average sales, per 100 leaflets sent, are shown in the table below. 
s1 s2 
A 0 19 
B 15 5 
C 10 12 
34. (1 mark) For the decision problem described by the table above, Alice’s 
guaranteed minimum average sales per hundred leaflets, if she didn’t know 
to which segment her customers belong when she sent out her leaflets, is: 
a) 65 
12 
b) 75 
12 
c) 85 
12 
d) 95 
12 
e) none of the above 
12 
35. (1 mark) Let p = P (s1) be the probability that a customer belongs to seg- 
ment s1. If p = 
7 
10 
, which leaflet would be most profitable? 
a) A 
b) B 
c) C 
d) a non-pure mixture of A and C 
e) none of the above 
36. (2 marks) Assume p = 7 
10 
, as in the previous question. Suppose Alice could 
hire an oracle who could predict to which segment each customer belongs 
with complete accuracy. If each unit sold makes a profit of $10, what is the 
highest rate, in dollars per 100 leaflets/customers, which Alice should pay 
for the oracle’s service? 
a) $29 
b) $42 
c) $23 
d) $37 
e) none of the above 
Questions 37 to 43 refer to zero-sum game matrix below. 
b1 b2 b3 b4 
a1 4 2 5 2 
a2 2 1 −1 −2 
a3 3 2 4 2 
a4 −6 0 6 1-6.0 
37. (1 mark) Which plays by the row player are best responses to column player’s 
b3? 
a) a1 only 
b) a2 only 
c) a3 only 
d) a4 only 
e) there are multiple best responses 
13 
38. (1 mark) Which plays by the row player are best responses to column player’s 
b2? 
a) a1 only 
b) a2 only 
c) a3 only 
d) a4 only 
e) there are multiple best responses 
39. (1 mark) Which plays by the row player are best responses to column player’s 
b1? 
a) a1 only 
b) a2 only 
c) a3 only 
d) a4 only 
e) there are multiple best responses 
40. (1 mark) Which plays by the column player are best responses to row player’s 
a2? 
a) b1 only 
b) b2 only 
c) b3 only 
d) b4 only 
e) there are multiple best responses 
41. (1 mark) How many saddle points does this game have? 
a) none 
b) one 
c) two 
d) three 
e) four 
14 
42. (1 mark) After simplification, how many strategies are left for the row player? 
a) none 
b) one 
c) two 
d) three 
e) four 
43. (1 mark) After simplification, how many strategies are left for the column 
player? 
a) none 
b) one 
c) two 
d) three 
e) four 
Questions 44 to 47 refer to the game matrix below. 
b1 b2 b3 
a1 2, 6 0, 4 4, 4 
a2 3, 3 0, 0 1, 5 
a3 1, 1 3, 5 2, 3 
26 
33 
11 
44. (1 mark) Which plays by the row player are best responses to the column 
player’s b1? 
a) a1 only 
b) a2 only 
c) a3 only 
d) there are two best responses 
e) there are more than two best responses 
15 
45. (1 mark) Which plays by the column player are best responses to the row 
player’s a3? 
a) b1 only 
b) b2 only 
c) b3 only 
d) there are two best responses 
e) there are more than two best responses 
46. (2 marks) Which plays by the row player are best responses to the column 
player’s mixed action 1 
3 
b1 
1 
3 
b2 
1 
3 
b3? 
a) a1 only 
b) a2 only 
c) a3 only 
d) there are two best responses 
e) there are more than two best responses 
47. (1 mark) Which plays by the column player are best responses to the row 
player’s mixed action 1 
2 
a1 
1 
4 
a2 
1 
4 
a3? 
a) b1 only 
b) b2 only 
c) b3 only 
d) there are two best responses 
e) there are more than two best responses 
Questions 48 to 53 refer to the problem below. 
16 
94 
1 
10 
m 
P 
D 
S 
Consider the football situation shown above, where Alice (blue #10) has 
three options: 
P pass to her team-mate (blue #9); 
D dribble closer to goal before shooting; or 
S shoot from where she is. 
The chances of scoring if Alice passes (P) to her team-mate are 3 in 10. Her 
chances of scoring by first dribbling closer (D) to goal and then shooting are 
5 in 10. Her chances of scoring by shooting from where she is (S) are 2 in 10. 
Bob, the goal-keeper (yellow #1), can choose to move (m) toward the ball 
as shown to reduce Alice’s scoring chances to 1 in 10 if she dribbles, at the 
expense of increasing her scoring chances by passing and shooting respectively 
to 5 and 3 in 10. 
48. (1 mark) Which is Alice’s Maximin pure action? 
a) P 
b) D 
c) S 
d) both P and D 
e) none of the above 
17 
49. (1 mark) Which is Bob’s Maximin pure action? 
a) m 
b) m 
c) both m and m 
d) neither m nor m 
e) none of the above 
50. (2 marks) How many pure strategy equilibria does this game have? 
a) 0 
b) 1 
c) 2 
d) 3 
e) none of the above 
51. (2 marks) Assuming that this situation were repeated many times (i.e., 
mixed strategies are allowed), the lowest value to which Bob could restrict 
Alice’s best response is: 
a) 7 in 10 
b) 6 in 10 
c) 5 in 10 
d) 4 in 10 
e) none of the above 
52. (1 mark) Let p = P (m) be the probability that the goal-keeper will move. 
Which value of p would restrict Alice’s best response to the least chance of 
scoring? 
a) p = 1 
3 
b) p = 3 
5 
c) p = 2 
3 
d) p = 2 
5 
e) none of the above 
18 
53. (1 mark) If mixtures are allowed for both players, which of the following is 
an equilibrium? 
a) (1 
3 
P2 
3 
D, 1 
3 
m2 
3 
m) 
b) (P,m) 
c) (D, 1 
3 
m2 
3 
m) 
d) (1 
2 
P1 
2 
D, 2 
3 
m1 
3 
m) 
e) none of the above 
End of exam