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)
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)
Chapter1: Making Economics Decisions
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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%2F45c224af-7552-42de-80ab-36c759b7e185%2F1f98858e-1daf-4e4a-b1f9-d86dc0b829d8%2Fsdc3nmh_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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