COVER PAGE FOR A WRITTEN EXAMINATION (ON CAMPUS)
Name of subject : Games and Economic Behavior
Subject code : 35V5B2-B-6
Date of examination : January 11, 2021
Length of examination : 3 hours
Lecturers : Prof. Dr. P.E.M. Borm
Phone : 013 4662430 (secr.)
Students are expected to conduct themselves properly during examinations and to obey any
instructions given to them by examiners and invigilators.
Firm action will be taken in the event that academic fraud is discovered.
SPECIFICS:
Open book exam no
Use of graphical calculator yes
Print on both sides yes
Scrap paper available yes
EXAM INSTRUCTIONS:
1. This exam consists of six exercises. The maximum number of score points is 100. For
each exercise, the maximal score is indicated separately.
2. Please provide complete solutions to each exercise. Each of your answers should be
clearly motivated.
3. Be aware that you have about 30 minutes per exercise. Some exercises should take
shorter however. Please have a look through the whole exam before you start working on
the exercises. In doing the exercises you do not have to follow the order of the questions
in the exam.
4. Do not forget to write down your name and student number (SNR, 7 digits) on each page
you hand in.
5. You can use scrap paper to work out the exercises. Scrap paper however will not be
graded.
6. After the exam, the exercises of the exam, the complete solutions, and a grading scheme
will become available via Canvas.
All students need to hand in the exam and their work (including scrap paper).
, Exam Games and Economic Behavior (35V5B2-B-6)
January 11, 2021
Duration: 3 hours
Please check that this exam consists of 6 exercises. The maximum total score is 100
points. For each exercise, the maximal score is indicated separately. Carefully explain
and/or motivate each of your answers. Please do not forget to put your name and stu-
dentnumber (SNR, 7 digits) on each page you hand in. Good luck!
Exercise 1 (16 points)
a) Consider the game v ∈ T U N with N = {1, 2, 3} given by
S ∅ {1} {2} {3} {1, 2} {1, 3} {2, 3} {1, 2, 3}
v(S) 0 c 0 0 24 24 12 36
with c ∈ R.
(i) Let c = 16. Using a picture, determine all extreme points of the core C(v).
(ii) Determine all values of c such that C(v) = ∅.
(iii) Determine all values of c such that C(v) has exactly three extreme points.
For each of these values of c, explicitly provide the corresponding extreme
points.
(iv) Determine all values of c such that v is S-equivalent to the game w ∈ T U N
given by
S ∅ {1} {2} {3} {1, 2} {1, 3} {2, 3} {1, 2, 3}
w(S) 0 −12 0 4 72 76 40 112
b) Prove explicitly that every superadditive and non-negative game v ∈ T U N is also
monotonic.
1
Name of subject : Games and Economic Behavior
Subject code : 35V5B2-B-6
Date of examination : January 11, 2021
Length of examination : 3 hours
Lecturers : Prof. Dr. P.E.M. Borm
Phone : 013 4662430 (secr.)
Students are expected to conduct themselves properly during examinations and to obey any
instructions given to them by examiners and invigilators.
Firm action will be taken in the event that academic fraud is discovered.
SPECIFICS:
Open book exam no
Use of graphical calculator yes
Print on both sides yes
Scrap paper available yes
EXAM INSTRUCTIONS:
1. This exam consists of six exercises. The maximum number of score points is 100. For
each exercise, the maximal score is indicated separately.
2. Please provide complete solutions to each exercise. Each of your answers should be
clearly motivated.
3. Be aware that you have about 30 minutes per exercise. Some exercises should take
shorter however. Please have a look through the whole exam before you start working on
the exercises. In doing the exercises you do not have to follow the order of the questions
in the exam.
4. Do not forget to write down your name and student number (SNR, 7 digits) on each page
you hand in.
5. You can use scrap paper to work out the exercises. Scrap paper however will not be
graded.
6. After the exam, the exercises of the exam, the complete solutions, and a grading scheme
will become available via Canvas.
All students need to hand in the exam and their work (including scrap paper).
, Exam Games and Economic Behavior (35V5B2-B-6)
January 11, 2021
Duration: 3 hours
Please check that this exam consists of 6 exercises. The maximum total score is 100
points. For each exercise, the maximal score is indicated separately. Carefully explain
and/or motivate each of your answers. Please do not forget to put your name and stu-
dentnumber (SNR, 7 digits) on each page you hand in. Good luck!
Exercise 1 (16 points)
a) Consider the game v ∈ T U N with N = {1, 2, 3} given by
S ∅ {1} {2} {3} {1, 2} {1, 3} {2, 3} {1, 2, 3}
v(S) 0 c 0 0 24 24 12 36
with c ∈ R.
(i) Let c = 16. Using a picture, determine all extreme points of the core C(v).
(ii) Determine all values of c such that C(v) = ∅.
(iii) Determine all values of c such that C(v) has exactly three extreme points.
For each of these values of c, explicitly provide the corresponding extreme
points.
(iv) Determine all values of c such that v is S-equivalent to the game w ∈ T U N
given by
S ∅ {1} {2} {3} {1, 2} {1, 3} {2, 3} {1, 2, 3}
w(S) 0 −12 0 4 72 76 40 112
b) Prove explicitly that every superadditive and non-negative game v ∈ T U N is also
monotonic.
1
