Consider a community inhabited by n goat-farmers, n > 1, each of whom owns goats that graze on a common field. If Farmer i, i = 1, . . . , n, sends gi goats to the field, then he/she earns i(g1, . . . , gn) = giV (G) 10gi , where G = g1 + + gn, and V (G) = 100 G.

(a) What is the total number of goats grazing in the field in a Nash equilibrium?

(b) Find the number of goats grazing if the field is owned by a single farmer.

(c) Why is your answer in part (a) larger than your answer in part (b)?