Prof. William H. Sandholm Department of Economics University of Wisconsin March 9, 2006
Midterm Exam Solutions Economics 713 1. Statement (A) is always true: ^ u1 (s1 , s2 ) min u1 (s1 , s2 ) for all s1
s2 S2 s1 S1 s1 S1 s2 S2
^ S1 and s2
S2. S2.
Prof. William H. Sandholm Department of Economics University of Wisconsin March 10, 2005 Midterm Exam Economics 713 1. (20 points) (i) State the Classic Folk Theorem. Be sure to present explicit definitions of any terminology related to payoffs that
Prof. William H. Sandholm Department of Economics University of Wisconsin March 13, 2008
Midterm Exam Economics 713 1. (35 points) Consider the extensive form game below:
1 O 4, 4 T 2 L 6, 2
(i) (ii) (iii) (iv)
I 1 B 2 R 0, 0 L 0, 0 R 2, 2
Comp
Prof. William H. Sandholm Department of Economics University of Wisconsin Spring 2008
Syllabus - Economics 713, Part 1
Course Description Economics 713 is a semester long course on game theory and information economics. I will teach the first half o
Economics 713, Final Exam
7PM, March 15, 22 503 (by Lones)
You must briefly justify your steps. Please do well!
There are 120 points in 120 minutes.
1. In The Treasure of the Sierra Madra, there is a large rock, under which [10]
is a treasure worth $100.
Econ713 Discussion Session Week2
Solutions
Michael and Ryoji
January 29, 2010
Exercise 5 (2002 Winter Prelim, Q4-a)
(i)
Observe that the set of pure strategies of each player, S1 and S2 , is
= f( A1 , A2 ) , ( A1 , D2 ) , ( D1 , A2 ) , ( D1 , D2 )g
= f (
Econ713 Discussion Session Week5
Solutions
Michael and Ryoji
February 20, 2010
Exercise 1
1. It is easy to nd that unique SPNE is f( L, T ), U g by backward induction.
2. The reduced normal form G () is as follows:
R
LT
LB
U
2, 2
3, 1
0, 5
D
2, 2
1, 0
1,
Econ713 Discussion Session Week10
Solutions
Michael and Ryoji
March 26, 2010
Exercise 3
1 (a)
It is a dominant strategy for each bidder to remain in the bidding until the price reaches
her value. So the bidder with the highest value wins and pays the seco
Econ713 Discussion Session Week11
Solutions
Michael and Ryoji
April 8, 2010
Exercise 1
1
Suppose rms offer a wage of w. All workers of type , with r ( )
w, will accept the
offer. Suppose there exists a 0 such that r 0 = w. Then all workers of type
0 wil
Econ713 Discussion Session Week14
Solutions
Michael and Ryoji
April 30, 2010
A note: monotone increasing wage over output
In an equilibrium, the wage schedule satises equation (1), i.e.
G 0 ( x s ( x )
f 0 ( x, a)
= + a
.
0 ( s ( x )
U
f ( x, a)
If the mo
Economics 713, Midterm Exam
February 23, 22 503 (by Lones, Anthony and Monica)
You must briefly justify your steps. Please do well!
There are 75 points in 75 minutes.
1. (5+10) An economy has just three firms f1 , f2 , f3 and just three employees
e1 , e2
Econ713 Discussion Session Week6
Solutions
Michael and Ryoji
February 26, 2010
Exercise 1
See the solution of 2002 midterm Q5.
Exercise 2
To nd sequential equilibria is similar to nding ones in extensive form games, i.e. do easy
parts rst followed by cons
Econ713 Discussion Session Week9
Solutions
Michael and Ryoji
March 18, 2010
Exercise 1
(i)
We use the way of guess and verify. Since the value of object is increased by 1/2, a
reasonable guess is as follows:
11
bi ( i ) = + i
22
We will show this is in fa
Economics 23 31, Midterm Exam
February 20, 2(29 -17) (by Tono and Lones)
You must briefly justify your steps. Please do well!
There are 75 points in 75 minutes Plus 20 bonus points.
1. Matching. Assume a continuum of rock stars and hipsters types in a
mat
Economics 713, Midterm Exam
February 19, 3 11 61 (by Tono and Lones)
You must briefly justify your steps. Please do well!
There are 100 points in 75 minutes. 25 of these points are bonus.
1. Matching. Assume that singers x and pianists y can match and for
Economics 713, Midterm Exam Solutions
February 19, 3 11 61 (by Tono and Lones)
You must briefly justify your steps. Please do well!
There are 100 points in 75 minutes. 25 of these points are bonus.
1. Matching. Assume that singers x and pianists y can mat
Economics 713, Midterm Exam Solutions
February 23, 22 503 (by Lones, Anthony and Monica)
You must briefly justify your steps. Please do well!
There are 75 points in 75 minutes.
1. (5+10) An economy has just three firms f1 , f2 , f3 and just three employee
Econ713 Discussion Session Week3
Solutions
Michael and Ryoji
February 11, 2010
Exercise 3
Please see Example 2.28 in Lecture Notes (p.41). The following gure shows the player 1s
best response correspondence.
X [10]
B
A
[5] 1/2X+1/2Y
5/11X+5/11Y+1/11Z
[51/
Prof. William H. Sandholm Department of Economics University of Wisconsin March 9, 2006
Midterm Exam Economics 713 1. (20 points) Let G be a two player normal form game, and suppose that players are only allowed to choose pure strategies. Only one
Prof. William H. Sandholm Department of Economics University of Wisconsin March 10, 2005 Midterm Solutions Economics 713 1. Let vi be player i's minmax value:
vi = min max ui (ai , a" i ) .
! " i #$ A" i ai #Ai
Let F = convex hull({u(a): a A}) an
Prof. William H. Sandholm Department of Economics University of Wisconsin March 13, 2007
Midterm Exam Solutions Economics 713 1. By the one-shot deviation principle, it is enough to check that there is no profitable one-shot deviation in any subgam
Prof. William H. Sandholm Department of Economics University of Wisconsin March 8, 2001 Midterm Exam Economics 713 1. (10 points) Consider the extensive form game pictured below. In this game, is it more appropriate to represent player 1's behavior
Prof. William H. Sandholm Department of Economics University of Wisconsin March 9, 2000 Midterm Exam Economics 713 1. (20 points) Suppose that players 1 and 2 play the game below, and that it is common knowledge between them that both of them are ra
Prof. William H. Sandholm Department of Economics University of Wisconsin March 12, 2002 Midterm Exam Economics 713 1. (10 points) Dave has preferences over lotteries which assign probabilities p = (pa, pb, p c) to three possible prizes: an apple, a
Prof. William H. Sandholm Department of Economics University of Wisconsin Spring 2000 Final Exam Solutions 1. Since we are only assuming common knowledge of rationality, we need to look for the rationalizable strategies. Since this is a two player ga
Prof. William H. Sandholm Department of Economics University of Wisconsin March 8, 2001 Midterm Exam Solutions 1. Behavior strategies are more appropriate here. In the extensive form drawn, player 1 is supposed to forget his initial behavior before c
Prof. William H. Sandholm Department of Economics University of Wisconsin March 12, 2002 Midterm Solutions Economics 713 1. Dave's preferences fail to satisfy the independence axiom. Let q = (0, 1, 0). Then 1 1 1 1 p 3 = 2 p1 + 2 q , and p 4 = 2 p 2
Lecture Notes on Game Theory-Typos
William H. Sandholm February 21, 2008 Section 1
location p. 11, l. -3 p. 13, 2nd fig. p. 14, l. 1 p. 14, l. -5 current text Ch xy (rear vertex) " " corrected text Ah xz " "
Section 2
location p. 20, l. 3 p. 20, l.
Prof. William H. Sandholm Department of Economics University of Wisconsin March 13, 2007
Midterm Exam Economics 713 1. (15 points) Suppose that two players repeatedly play the following normal form game: T 3, 3 1, 2 4, -2 2 M 2, 1 1, 1 3, -1 B -2,