Suppose that the share of total production consumed by player i is x / x+(n1)y, where x is player i's level of conflict and y is the level of conflict chosen by the other n 1 players. Thus, utility to player 1 is u = (x / x +(n1)y) A[nw-x-(n-1)y], where w > 0 the endowment of each player and A >1 is a technology parameter. (a) Find the symmetric Nash equilibrium level of conflict, x* and show how conflict as a share of the endowment (x*/w) varies with n. Hint: First derive au/əx , set it equal to zero for a maximum, and then let y= =x* and solve for x*. (b) Why does the equilibrium level of conflict depend upon the number of people in society, n, but not the state of technology, A
Suppose that the share of total production consumed by player i is x / x+(n1)y, where x is player i's level of conflict and y is the level of conflict chosen by the other n 1 players. Thus, utility to player 1 is u = (x / x +(n1)y) A[nw-x-(n-1)y], where w > 0 the endowment of each player and A >1 is a technology parameter. (a) Find the symmetric Nash equilibrium level of conflict, x* and show how conflict as a share of the endowment (x*/w) varies with n. Hint: First derive au/əx , set it equal to zero for a maximum, and then let y= =x* and solve for x*. (b) Why does the equilibrium level of conflict depend upon the number of people in society, n, but not the state of technology, A
Chapter1: Making Economics Decisions
Section: Chapter Questions
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![Suppose that the share of total production
consumed by player i is x / x+(n1)y, where x
is player i's level of conflict and y is the level
of conflict chosen by the other n 1 players.
Thus, utility to player 1 is u = (x / x +(n1)y)
A[nw-x-(n-1)y], where w > 0 the
endowment of each player and A >1 is a
technology parameter.
(a) Find the symmetric Nash equilibrium
level of conflict, x* and show how conflict
as a share of the endowment (x*/w) varies
with n. Hint: First derive du/əx , set it equal
to zero for a maximum, and then let y= X
=x* and solve for x*.
(b) Why does the equilibrium level of
conflict depend upon the number of people
in society, n, but not the state of
technology, A](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e3b8cd6-52e5-46a8-9d89-aa92018c5fd4%2Ff3186b35-9b15-4a6b-80ef-1b62f689d215%2Fp5iwwnh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that the share of total production
consumed by player i is x / x+(n1)y, where x
is player i's level of conflict and y is the level
of conflict chosen by the other n 1 players.
Thus, utility to player 1 is u = (x / x +(n1)y)
A[nw-x-(n-1)y], where w > 0 the
endowment of each player and A >1 is a
technology parameter.
(a) Find the symmetric Nash equilibrium
level of conflict, x* and show how conflict
as a share of the endowment (x*/w) varies
with n. Hint: First derive du/əx , set it equal
to zero for a maximum, and then let y= X
=x* and solve for x*.
(b) Why does the equilibrium level of
conflict depend upon the number of people
in society, n, but not the state of
technology, A
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