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

use a zero tolerance policy on this aspect of your answers.

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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

your student id.

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,

but include C(fz1; z2; z3g) = fz1g? Explain your answers.

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)

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