Find the mixed nash equilibrium
S1
S2
S3
T1
3,5
4,3
6,4
T2
2,4
6,6
4,3...
Find the mixed nash equilibrium
S1
S2
S3
T1
3,5
4,3
6,4
T2
2,4
6,6
4,3
T3
5,3
5,5
2,1
Question 1: Roll two fair dice. Then the sample space S is the
following.
S =...
Question 1: Roll two fair dice. Then the sample space S is the
following.
S =
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let E be the event that the sum of the dice is odd, let F be the
event that the first die lands on 1,
and let G...
Compute the Nash equilibria of the following location game.
There are two
people who simultaneously select...
Compute the Nash equilibria of the following location game.
There are two
people who simultaneously select numbers between zero and one.
Suppose
player 1 chooses s1 and player 2 chooses s2 . If si = sj , then
player i gets a
payoff of (si + sj )/2 and player j obtains 1 − (si + sj )/2,
for i = 1, 2. If
s1 = s2 , then both players get a payoff of 1/2.
1. Two dice are rolled. There are 36 possible outcomes, the
sample space is:
(1,1) (1,2)...
1. Two dice are rolled. There are 36 possible outcomes, the
sample space is:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4)
(2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3)
(4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2)
(6,3) (6,4) (6,5) (6,6)
A = ‘second roll is a 6’
B = ‘sum of two dice equals 7’
C = ‘sum of two dice equals 3’
a. What is P(B|A)?
b. What is...
. Present your formal analysis carefully and compute the Nash
equilibria of the following location game...
. Present your formal analysis carefully and compute the Nash
equilibria of the following location game in pure strategies. There
are two people who simultaneously select numbers between zero and
one. Suppose player 1 chooses s1 and player 2 chooses s2. If si
< sj , then player i gets a payoff of (si+sj ) 2 and player j
obtains 1 − (si+sj ) 2 , for i = 1, 2. If s1 = s2, then both
players get a...
Consider the following simultaneous-move game:
Column
L
M
N
P
Row
U
(1,1)
(2,2)
(3,4)
(9,3)...
Consider the following simultaneous-move game:
Column
L
M
N
P
Row
U
(1,1)
(2,2)
(3,4)
(9,3)
D
(2,5)
(3,3)
(1,2)
(7,1)
(a) Find all pure-strategy Nash equilibria.
(b) Suppose Row mixes between strategies U and D in the
proportions p and (1 − p). Graph the payoffs of Column’s four
strategies as functions of p. What is Column’s best response to
Row’s p-mix?
(c) Find the mixed-strategy Nash equilibrium. What are the
players’ expected payoffs?
9K)Below is a list of all possible outcomes in the experiment of
rolling two die. (If...
9K)Below is a list of all possible outcomes in the experiment of
rolling two die. (If the grid pops up twice, pay attention to only
one table. Having formatting issues, apologies! And thank you for
your help!
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6
Determine the following probabilities. Write your answers...
Find two nash equilibria of the game
L
C
R
U
1,-1
0,0
-1,1
M
0,0...
Find two nash equilibria of the game
L
C
R
U
1,-1
0,0
-1,1
M
0,0
1,1
0,0
D
-1,1
0,0
1,-1
The following data are given for the two experiments:
n1=14, = 17, s1=1.22
n2=16, = 19, s2=1.34
Find...
The following data are given for the two experiments:
n1=14, = 17, s1=1.22
n2=16, = 19, s2=1.34
Find a 98% confidence interval for μ2-μ1 ,
as assuming normal populations with equal variances.