Anarchy Equilibria:

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 u/x , 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?

(c) Assume that each player's equilibrium production is Ak = A(w - x*). Show your equilibrium utility u* varies with n.