Please help me with this question. Thank you.

There are n 2 2 identical fishermen who independently decide how much to fish in a public lake. The utility to each fisherman i, i = 1, . ..,n, is given by xi(b - c(X)), where x; 2 0 is the amount of fishing i chooses, b > 0 is the constant marginal benefit of fishing, and c is the marginal cost of fishing. Also, c is a twice-differentiable function of the total amount of fishing X = _,_j x; and satisfies c(0) = 0, c' > 0 and c' 2 0. (a) What is the strategy space of this game? What is a Nash equilibrium of this game? Show that this game has a unique Nash equilibrium. (b) Show that in the socially optimal solution to the this problem (where the gov- ernment wants to maximize the sum of everyone's utility), the total amount of fishing is less than that in the Nash equilibrium