Problem Set 7 Solution
17.881/882
November 8, 2004
1
Gibbons 2.3 (p.131)
Let us consider the three-period game first.
1.1
The Three-Period Game
The structure of the game as was described in section 2.1D (pp.68-71). Let us
solve the game backwards.
1.1.1
S
Problem Set 3 Solution
17.881/882
October 18, 2004
1
Morrow
4.11 (pp.107-8)
Note that the ideal point of the median voter is yn , and that the mid-point
between x1 and x2 is (x1 + x2 )/2
a) Partition the set of ideal points and call nl = |cfw_i|yi < (x1 +
Problem Set 6 Solution
17.881/882
November 5, 2004
1
Gibbons 2.4
Let us find the best-response for player 2.
If c1 R = U2 = V
c2
If c2 < 0 = U2 = V c22 c2 R c1 and U2 = 0 c2 < R c1 .
From this, we have
BR2 (c1 ) =
0
if c1
R or c1 < R V
R
c1
if R V <c1 <
Problem Set 8 Solution
17.881/882
November 22, 2004
1
Morrow 5.7 (page 143)
The Solution
a)
The set of stable values is YSQ [4, 7]
b)
For YSQ < 3 or YSQ > 7, the outcome is 5; for YSQ (3, 4), the outcome is
8 YSQ .
Details on the Solution
The solution is
Problem Set 4 Solution
17.881/882
October 26, 2004
1
Gibbons 2.1 (p.130)
This is a dynamic game of perfect information, we will use backward induction
to solve.
We start at the final stage. The parents objective is
max V (Ip (A) B) + kU (Ic (A) + B)
B
The
Problem Set 10 Solution
17.881/882
December 6, 2004
1
Gibbons 3.2 (p.169)
1.1
Strategy Spaces
Firm 1 has two types or two information sets and must pick an action for each
type. Firm 2 has only one type and can only pick one action.
The strategy spaces ar
Problem Set 11 Solution
17.881/882
December 9, 2004
1
1.1
Gibbons 4.1 (p.245)
Game A
The normal form representation of this game is the following:
L0
R0
L
(4, 1) (0, 0)
M (3, 0) (0, 1)
R
(2, 2) (2, 2)
The pure-strategy Nash Equilibria are (L, L0 ) and (R,