Round 34,699 to the nearest ten thousand
2 answers:
You might be interested in
Answer:
a) attached below
b) ( T,T )
c) The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )
d) The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )
while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 )
Step-by-step explanation:
A) write down the game in matrix form
let: E = exit at the industry immediately
T = exit at the end of the quarter
N = exit at the end of the next quarter
matrix is attached below
B) weakly dominated strategies is ( T,T )
C) Find the pure-strategy Nash equilibria
The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )
D ) Find the unique mixed-strategy Nash equilibrium
The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )
while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 ) since T is weakly dominated then the mixed strategy will be NE
Assume that P is the probability of firm 1 exiting immediately ( E )
and q is the probability of firm 1 staying till next term ( N ) ∴ q = 1 - P.
hence the expected utility of firm 2 choosing E = 0 while the expected utility of choosing N = 4p - 2q .
The expected utilities of E and N to firm 2 =
0 = 4p - 2q = 4p - 2 ( 1-p) = 6p -2 which means : p = 1/3 , q = 2/3
Let 
be the tickets that the adults bought, and
be the tickets that children bought.
From the problem we have the system of linear equations:
The first thing we are going to do to solve our system, is replacing equation (2) in equation (1), and then, solve for
Now that we have the number of tickets that the adults bought, lets replace that value in equation (2):
Last but not least, to find the total number of tickets, we are going to add and 
:
We can conclude that <span>Northwest High School's senior class sold 632 raffle tickets.</span>
From the problem we have the system of linear equations:
The first thing we are going to do to solve our system, is replacing equation (2) in equation (1), and then, solve for
Now that we have the number of tickets that the adults bought, lets replace that value in equation (2):
Last but not least, to find the total number of tickets, we are going to add
We can conclude that <span>Northwest High School's senior class sold 632 raffle tickets.</span>