UNIVERSITY OF SOUTHAMPTON ECON6025W1

SEMESTER 2 EXAMINATIONS 2017/18

ECON6025 Topics in Economic Theory

Duration: 120 mins

This paper contains 5 questions

Answer FOUR questions. All questions carry equal weight.

An outline marking scheme is shown in brackets to the right of each question.

Only University approved calculators may be used.

A foreign language direct ‘Word to Word’ translation dictionary (paper version)

ONLY is permitted. Provided it contains no notes, additions or annotations.

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2 ECON6025W1

1. Consider an agent who takes an action after receiving some in-

formation. A decision problem is a tuple (S,Π, C, u, p), where

S is the state space, Π is the partition, C is the set of actions,

u : S × C → R is the utility function and p is the prior over

S. Show that if partition Π1 is finer than partition Π2 then decision

problem A = (S,Π1, C, u, p) is more valuable than decision problem

B = (S,Π2, C, u, p).

2. In the strategic bargaining model of Rubinstein, show that if the

utility of player i, ui, is differentiable and axioms A0-A6 hold, we

have that δu′i(xi) < u

′

i(vi(xi, 1)), where vi(xi, 1) > 0 is the present

value at period 0 of getting xi at period 1. Moreover, show that if

ui is concave then u

′

i(xi) < u

′

i(vi(xi, 1)).

3. Consider a state space S = {s1, s2, s3, s4, s5}. There are two

agents, i = 1, 2, with a common prior p = (0.3, 0.1, 0.2, 0.3, 0.1).

Agent 1 has information partition Π1 = {{s1, s2}, {s3}, {s4, s5}}

and 2 has information partition Π2 = {{s3, s2}, {s4}, {s1, s5}}.

(a) Given common prior p and information structures Π1,Π2, derive

types t1(s), t2(s), for each s ∈ S.

(b) Given the types t1 and t2 that you have derived in the previous

question, find probability distribution p1 ∈ ∆S that is a prior

for agent 1 and p2 ∈ ∆S that is a prior for agent 2, where

p1, p2 6= p. Is there a common prior, different from p, that

assigns positive probability to all states?

(c) Suppose that 1’s prior is p1 = (0.2, 0.1, 0.3, 0.2, 0.2) and 2’s

prior is p2 = (0.3, 0.1, 0.2, 0.2, 0.2). Find an ex ante bet and an

interim bet.

4. Show that in a bargaining game of alternating offers one can find,

for every (x1, x2) ∈ X = {(x1, x2) ∈ R2+ : x1 + x2 ≤ 1}, a Nash

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3 ECON6025W1

equilibrium where player one gets x1 in period 0. Explain why the

Nash equilibrium you construct may not be subgame perfect.

5. Consider a state space S and two agents, 1 and 2, with information

partitions Π1 and Π2, respectively. Describe what are types. Define

what is interim betting among the two agents. Show that there is

a common prior if and only if there is no interim betting.

END OF PAPER

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Social Sciences

Examination Feedback

2017/2018

Module Code & Title: ECON6025 Topics in Economic Theory

Module Coordinator: Spyros Galanis

Mean Exam Score: 61.21

Percentage distribution across class marks:

UG Modules

1 st (70% +)

2.1 (60-69%)

2.2 (50-59%)

3rd (40-49%)

Fail (25-39%)

Uncompensatable Fail

(<25%)

PGT Modules

70% + 37.5%

60-69% 12.5%

50-59% 50%

<50% 0%

Overall strengths of candidates’ answers:

Students seemed on average to have a good grasp of the relevant models and notions. They did well

in the numerical-type questions. They were also able to explain well the relevant theory.

Overall weaknesses of candidates’ answers:

When asked to prove a claim, some students had problems providing a formal argument and using

math notation.

Pattern of question choice:

The most common pattern of choice was 1,2,3 and 5.

Issues that arose with particular questions:

Some students misunderstood the relevant bargaining model when answering question 4. Although

most students were able to identify the correct Nash equilibrium in question 4, they were not able to

convincingly argue why it is a Nash equilibrium. In 3c, most students were not able to argue

whether an interim bet exists. In question 1, most students did not give a general proof.

Further comments not covered above:

The mean mark is within reasonable range, and the mark distribution is slightly skewed towards the

number of firsts, which can be explained by the very small number of students and the

numerical/mathematical nature of the questions.

Discipline vetting completed By (Name): Hector Calvo Date: 13/06/2018

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