# Game Theory Assignment | Essay Help Services

ECN 190A,
Making Better Decisions
Professor
Spring 2020
Instructions:
This is an open book exam. This exam is worth 100 points.
You can use your own calculators in this exam. When in doubt, round
numeric responses to two decimal places.
Please do not communicate with anyone else, in any way, while attempting
the exam.
You must show your work on every question that requires a calculation.
We will award partial credit as appropriate. Correct results without ade-
quate work will receive little or no credit.
The questions would often refer to the last and second last digits of your
student id as d and c respectively. If your student id is 1234567, then the
last digit of your student id is d = 7 and the second last digit of your
student id is c = 6. All questions hinge on you correctly understanding
this, so please make sure you understand this before moving on to the
questions. To deter students using unfair means on the exam, we would
1
Question 1) (15 points)
Find the Rank Dependent Utility of the lottery (10; :3; 5; :2; d; :5), when g(p) =
p2 and u(x) = x2 where d is the last digit of your student id. (note that you
rst need to rank the outcomes in order, and that depends on the value of d!)
Question 2) (15 points)
Consider three price-commodity pairs given by p1 = (2; 2; 4), p2 = (4; 2; 2),
p3 = (2; 4; 2 + c + 2), x1 = (1; 0; 0), x2 = (0; 1; 0), x3 = (0; 0; 1), where c is
the second last digit of your student id. Does the data satisfy WARP? Does it
satisfy GARP? Show all your steps.
Question 3) (15+15+10 points) Suppose in a beauty contest game, each player
chooses si 2 f100; 101::::; 200 + 10dg = Si, p = 3
2 , where d is the last digit of
i) What strategies can you eliminate through two rounds of iterated elimination
of weakly dominated strategies?
ii) What would levels 1, 2, 3 and 4 play in this game, according to level-k the-
ory?
iii) What is the Nash Equilibrium of this game? Can you prove that this would
be a Nash Equilibrium?
Question 4) (5+5+10 points)
Suppose, X = fz1; z2; z3; z4g, and C(fz1g) = fz1g;C(fz2g) = fz2g;C(fz3g) =
fz3g;C(fz1; z2g) = fz1; z2g;C(fz2; z3g) = fz2g;C(fz1; z3g) = fz3g; C(fz1; z2; z3g) =
fz1; z2; z3g. Does this satisfy Sen’s ? Does this satisfy Sen’s ? How would
your answers change if we removed C(fz1; z2; z3g) = fz1; z2; z3g from this data,
Question 5) (10 points) Choose the correct alternative:
When is Sen’s and a test for rationality of a dataset?
(i) when you observe complete data (a complete choice correspondence)
ii) when you observe incomplete data (an incomplete choice correspondence)
iii) both (i) and (ii)
2

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