ECO2030 Unit 2: Problem Set 2
1. In the discrete setting discussed in class, show that MLRP implies FOSD. Give a counterexample that the reverse is not true.
2. Formulate MLRP and FOSD when outcome space is continuous (say an interval of R).
Show that MLR

ECO2030 Unit 2: Problem Set 1
1. Consider the following variation of the Akerlof model discussed in class. The quality of
the used car is randomly drawn from a uniform distribution [, 2 + ], with > 0.
The sellers reservation value r () given by r () = . C

Economics 2030
Winter 2014
Martin J. Osborne
Problem Set 7
1. Two people are initially n 3 meters apart, where n is an integer. Each
has a gun containing a single bullet. They move alternately, starting
with player 1. If, on her turn, the distance between

Economics 2030
Winter 2014
Martin J. Osborne
Problem Set 12
1. Exercise 216.1 in the book.
2. Exercise 217.3 in the book.
3. Find all the weak sequential equilibria of the extensive game with imperfect information in Figure 1.
A
1
N
1
2
D
A
0, 0
100, 150

Economics 2030
Winter 2014
Martin J. Osborne
Problem Set 11
1. Exercise 146.1 in the book.
2. Consider the discounted innitely repeated game of the Prisoners
Dilemma in Figure 1.
C
D
C
x, x
y, 0
D
0, y
1, 1
Figure 1. The general Prisoners Dilemma in Exerc

Economics 2030
Winter 2014
Martin J. Osborne
Problem Set 10
1. Consider the innitely repeated game of the strategic game in Figure 1, where the parameters x and y satisfy 1 < x < y and each
player has the same discount factor (with 0 < < 1). Suppose that

Economics 2030
Winter 2014
Martin J. Osborne
Problem Set 8
1. Consider the following variant of the bargaining game of alternating
offers, when the size of the pie is $100. Neither player discounts future
payoffs (i.e. both discount factors are equal to 1

Economics 2030
Winter 2014
Martin J. Osborne
Problem Set 9
1. Show that Nashs bargaining solution satises the INV axiom.
2. (a) For any bargaining problem (U, d), let f (U, d) be the point in U
on the 45 line through d for which v1 (and v2 ) is as large a

Economics 2030
Winter 2014
Martin J. Osborne
Problem Set 6
1. Find the subgame perfect equilibria of the game in Figure 1.
1
C
D
2
E
2, 1
2
G
F
2, 0
1, 1
H
1, 0
Figure 1. The game in Problem 1.
2. Consider a nite extensive game with perfect information in

Economics 2030
Winter 2014
Martin J. Osborne
Problem Set 1
1. Consider Cournots oligopoly game in the case of an arbitrary nite
number n of rms. Assume that the inverse demand function P takes
the form
Q if Q
P(Q) =
0
if Q >
and the cost function of ea