Econ 511
Solutions to Assignment 4
As many questions are straight from the lectures I have not typed the solutions to these.
1. Consider a prisoners dilemma with stage game payos
C
D
c
2; 2
3; 0
d
0; 3
1; 1
played twice.
1. Sketch the extensive form.
Solu
9
A Class of Dynamic Games of Incomplete Information: Signalling Games
In general, a dynamic game of incomplete information is any extensive form game in which
at least one player is uninformed about some other players type and where there are some
sequen
6
Extensive Form Games
6.1
Example: Representing a Simultaneous 2 2 Game
Alice
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"HH
"
"
H
HH
O "
"
"
"
H
"
H
"
"
H
Bob
"
"
HH
"
o " QQ h
o
Hh
"
HH
Q
"
Q
"
"
2
0
0
1
1
0
0
2
Figure 1: The Battle of the Sexes in Extensive Form
So far we have described game
8
Games with Incomplete Information (Bayesian Games)
8.1
Example of a Static Game of Incomplete Information: Cournot
Duopoly with Unknown Cost
Suppose that rm 1 and rm 2 produce a homogenous good with inverse demand p (q) =
max f2
q; 0g : Also suppose tha
3
Weakly Dominant and Dominated Strategies
Recall that we said that s0i is strictly dominated by s00 if ui (s0i ; s i ) < ui (s00 ; s i ) for every
i
i
s
2 S i . An obvious weakening of the concept is to allow for weak instead of strict
i
inequalities:
De
7
Repeated Games
7.1
Example: A Prisoner Dilemma Played Twice
s
Suppose the rules are as follows. In period 1, the players play
D
C
d 1; 1 3; 0 :
c 0; 3 2; 2
After the rst period, the players observe the outcome and then play the game a second
time.
In th
5
Mixed Strategies
5.1
5.1.1
Example: Matching Pennies
The Story
Alice and Bob debate whether to go to see Philomena (the top choice for Alice) or 47 Ronin
(the top choice for Bob). As they cannot agree, they decide to settle the outcome by playing
a game
Econ 511
February 18 2014
Peter Norman
Assignment 5
Due February 25.
1. Consider a Cournot game with inverse demand p (y) = 12
y and constant marginal cost c = 3:
1. Find the static Nash equilibrium in the one shot Cournot game and nd the cartel outcome t
13
Legislative Bargaining
One of the most popular legislative models is a model due to Baron & Ferejohn (1989). The
model has been used in applications where the role of committees have been studies, how
the legislative outcome depends on characteristics
Econ 511
February 25 2014
Peter Norman
Assignment 6
Due March 4.
1. Consider the following dynamic game of incomplete information. At time 0 nature draws the type of
player 1 (the sender), which may be strongor weak[say with a 50/50 chance of either type]
Econ 511
February 25 2014
Peter Norman
Assignment 7
Due April 1.
1. Consider the following bargaining game between two players splitting a dollar. First, player two writes
down a number in [0; 1] on a piece of paper. Then, player 1 makes an oerwithout bei
1
Games in Normal Form (Strategic Form)
A Game in Normal (strategic) Form consists of three components:
1. A set of players, N = f1; :; ng
2. For each player, a set of strategies (called actions in textbook) Si : The interpretation
is that this should be
13
Bargaining
13.1
The Ultimatum Game
13.1.1
The Extensive Form
Consider the following game:
There are two players, 1,2.
First, player 1 proposes a division of a dollar. That is, a pair x = (x1 ; x2 ) such that
x1 + x2 = 1
After observing the proposal, pl