1
Homework #3 solutions / IEOR4407
1. (a) What is the probability that the proposition will pass, as a function of and ?
Solution: The proposition passes when: (i) When A votes the proposition passes
1
Homework #1 solutions / IEOR4407
1.1. (Gibbons 1.2) Elimination of dominated strategies gives us the above table below:
T
M
B
L
(2,0)
(3,4)
(1,3)
C
(1,1)
(1,2)
(0,2)
R
(4,2)
T
(2,3)
M
(3,0)
L
(2,0)
IEOR E4407: Game-Theoretic Models of Operations
Irene Lo
October 16, 2016
HW 5 (PRACTICE ONLY)
1. Problem 9.2 from Tadelis:
Centipedes revisited: Two players are playing two consecutive games. First,
1
Homework #2 solutions / IEOR4407
1. (Gibbons 1.11) Using Problem 1.7 (Gibbons 1.14), we can eliminate dominated strategies before
computing NE. Hence using solution to 1.1 we start with
L
(2,0)
(3,4
1
Homework #1 solutions / IEOR4407
1.1. (Gibbons 1.2) Elimination of dominated strategies gives us the above table below:
T
M
B
L
(2,0)
(3,4)
(1,3)
C
(1,1)
(1,2)
(0,2)
R
(4,2)
T
(2,3)
M
(3,0)
L
(2,0)
Homework #4 solutions / IEOR4407
1
1. (Gibbons 3.2) Firm 1 has two types and has to pick an action for each type. Firm 2 has only one
type and has to pick one action. Hence the strategy space for rm 1
Sketch of sample nal solutions / IEOR4407
1
1. An ecient allocation is the one that maximizes the sum of the utilities. It is a combinatorial
problem, but here its easily seen that giving both items t
1
Homework #5 solutions / IEOR4407
1. (Gibbons 3.6) Following the arguments developed in class. Let bidder i bid bi = Si (vi ), where vi
are drawn from a Uniform(0, 1) distribution, and bidder i sees
1
Homework #2 solutions / IEOR4407
1. (Gibbons 1.11) Using Problem 3 below (Gibbons 1.14), we can eliminate dominated strategies
before computing NE. Hence using solution to 1.2 we start with
L
(2,0)
1
Homework #6 solutions / IEOR4407
1 Revenue in this Auction:
x
b(y)f (y)dy + b(x)[1 F (x)]
m(x) = P (Y < x)E[b(Y )|Y < x] + P (Y > x)E[b(x)|Y > x] =
0
By Revenue Equivalence,
x
x
b(y)f (y)dy + b(x)[1
Problem Set 2 Solution
17.881/882
October 10, 2004
1
Gibbons 1.10 (p.50)
As a general rule, you should try to minimize the algebraic calculations that
you make. Use the concepts to simplify the proble
1
Homework #7 solutions / IEOR4407
1 (a) An ecient allocation assigns the TV to the roommates only if the sum of their values, va +vb
is greater than or equal to vc = 100. To think about this problem,
IEOR E4407: Game-Theoretic Models of Operations
Jay Sethuraman
September 19, 2016
HW 1 (due Wednesday, 09/21) (You should read Chapters 1, 3 and 4 of Tadelis, available
online.)
1. You have room for u
IEOR E4407: Game-Theoretic Models of Operations
Irene Lo
October 14, 2016
HW 4 (due Wednesday, 10/12)
1. Imagine a two-player game that proceeds as follows. A pot of money is created with $6
in it ini
IEOR E4407: Game-Theoretic Models of Operations
Irene Lo
October 14, 2016
HW 3 (due Wednesday, 10/05) (You should read Chapter 6 of Tadelis, available online.)
1. Problem 6.8 from Tadelis:
Market entr
IEOR E4407: Game-Theoretic Models of Operations
Jay Sethuraman
September 22, 2016
HW 2 (due Wednesday, 09/28) (You should read Chapters 5 and 6 of Tadelis, available
online.)
1. Problem 4.10 in Tadeli
Midterm solutions / IEOR4407
1
1. (a) The LP formulation for player 1 is
Max z
T
ze pT U
p0
T
p e=1
If we change the problem to U = U c1 eeT , where eeT is a matrix of all ones and c1 is
a constant va
Homework #5 solutions / IEOR4407
1
1. (Gibbons 3.1) Refer to section 3.1 of the text.
2. (Gibbons 3.2) Firm 1 has two types and has to pick an action for each type. Firm 2 has only one
type and has to
1
Homework #4 solutions / IEOR4407
1. (Gibbons 2.6) Each rm i wants wants to choose qi to maximize (P (Q) c)qi .
First, lets x rm 1s choice q1 . Then we look at rm 2 and 3s problem. We look at rm 3 rs
1
Homework #3 solutions / IEOR4407
1. (a) What is the probability that the proposition will pass, as a function of and ?
Solution: The proposition passes when: (i) When A votes the proposition passes