Determine the intervals on which the function is increasing, decreasing, and constant.
2 answers:
Answer:
b. Increasing x > 0; Decreasing x < 0
Step-by-step explanation:
We have been given graph of a function. We are asked to find the intervals on which our function is increasing and decreasing.
We know that when graph of function is going upwards from left to right then the graph is increasing.
When graph of function is going downwards from left to right then the graph is decreasing.
Upon looking at our given graph, we can see that for x values less than 0, the graph is going downwards from left to right, therefore, our function is decreasing on interval .
We can see from our given graph that for x values greater than 0, the graph is going upwards from left to right, therefore, our function is increasing on interval .
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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
