Econ 521 - Discussion Section
Week 8
Exercises
1. Voting by alternating veto - [Based on Osborne 163.2]
Two people select a policy that affects them both by alternately vetoing policies until
only one remains. First person 1 vetoes a policy. If more than
GAME THEORY AND ECONOMIC APPLICATIONS (ECON 521), SPRING 2016
UNIVERSITY OF WISCONSIN-MADISON, PROF. MARZENA ROSTEK
PROBLEM SET 7
Due in (=before) class on March 29 (Tuesday), 2016
Question 1: Summer internship in DC A DC-based NGO plans on hiring an inte
GAME THEORY AND ECONOMIC APPLICATIONS (ECON 521), SPRING 2016
UNIVERSITY OF WISCONSIN-MADISON
SOLUTIONS: PROBLEM SET 1
Question 1
a. There are no strictly dominated strategies for either player. This is easy to see: all choices give
each player the same p
GAME THEORY AND ECONOMIC APPLICATIONS (ECON 521), SPRING 2016
UNIVERSITY OF WISCONSIN-MADISON
SOLUTIONS: PROBLEM SET 3
Question 1
(a) Fish game: In b., L<S<0.5*(H+L) and this is similar with the Prisoners Dilemma.
NE is (P,P).
In c., for S<L: NE are (E,P)
GAME THEORY AND ECONOMIC APPLICATIONS (ECON 521), SPRING 2016
UNIVERSITY OF WISCONSIN-MADISON
SOLUTIONS: PROBLEM SET 4
Question 1.
Game:
Players: N players, i=1,.N
Strategies: qi 0 , i=1,.N
Payoffs=Profits:
i
(q1 .q N )
(i) FOC (q1): a b(q1
P(Q)qi
. q N )
GAME THEORY AND ECONOMIC APPLICATIONS (ECON 521), SPRING 2016
UNIVERSITY OF WISCONSIN-MADISON, PROF. MARZENA ROSTEK
PROBLEM SET 6
Due in (=before) class March 17, 2016
Question 1: Strategies in extensive-form games
(a) Write down the strategies for both p
ECON 521, Discussion Section 10 SOLUTION
TA: Aiday Sikhova ([email protected]) ; Date: 11/14/15
1. Consider a game where player 1 rst decides to stay out or enter. Conditional on entry he
then decides to play T or B. Player 2 only observes the entry decisi
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2011
Second Midterm Exam
1. (30 points)
Consider the following normal form game G:
2
L
C
T 0, 0 1, 1
1
B 4, 4 3, 3
R
5, 5
1, 1
First suppose that players may only choose pure strategies.
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2011
Second Midterm ExamSolution
1. (i) Player 1s maxmin payo is maxcfw_0, 1 = 1.
(ii) Player 1s minmax payo is mincfw_4, 3, 5 = 3.
(iii) Drawing the graphs of u1 (1 , L), u1 (1 , C), an
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2010
Second Midterm ExamSolution
1. (i) Player is payo function is
2s (3 s ) (s )2 + 1)
i
j
i
ui (si , s j ) =
0
if si > 0,
if si = 0.
(ii) The rst case of ui (si , s j ) above is maxim
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2011
First Midterm Exam
1. (20 points)
We present Jane with an urn containing 90 balls. We tell her that 30 of the balls are red,
and that each of the remaining 60 balls is either blue o
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2010
First Midterm Exam
1. (15 points)
Let G = cfw_I; S1 , . . . , Sn ; u1 , . . . , un be a normal form game.
(i) Dene i , the set of mixed strategies of player i, and , the set of mix
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2010
Final Exam Solutions
1. (35 points)
(i) We can summarize player 1s strategy by his choice of x1 (since x2 = 1 x1 ), in
which case his strategy set is [0, 1]. Player 2s strategies ar
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2010
First Midterm ExamSolution
1. (i) Player is mixed strategy set is
i = Si = cfw_i : i (si ) 0 for all si Si and
si Si
i (si ) = 1.
The set of mixed strategy proles is = iI i .
(ii) P
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2011
First Midterm ExamSolution
1. (20 points)
Janes stated preferences are not consistent with her being a Bayesian rational decision
maker. A Bayesian rational decision maker maximizes
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2010
Second Midterm Exam
1. (30 points)
Two competing salesmen each choose levels of eort si Si = [0, 3] to exert. The
revenue earned by salesman i as a function of both eort levels is 2
Prof. William H. Sandholm
University of Wisconsin
Economics 521
Fall 2010
Final Exam
1. (35 points)
Two players bargain over a dollar. The bargaining takes place over at most k 1
rounds. In each round, one player is the proposer, and the other is the resp