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)?

NOW Consider the same framework: There are 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, he/she earns

i(g1, . . . , gn) = giV (G) 10gi, where V (G) = 15. (So value per goat is constant at 15.)

(d) A Nash equilibrium does not exist. Why?

(e) The phenomenon "Tragedy of the Commons" does not occur here. That is the cattle

on this common are not so puny and stunted? Why?