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
Problem 1QTC
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