4. Let $q_i$ be the number of sheep that herder $i=1,2$ grazes on the commons.\ Suppose that the per-sheep value of grazing on the commons is\ $v(q_1, q_2) = 100 - (q_1 + q_2)$. Then, the payoffs of the two herders are\ $u_1(q_1, q_2) = q_1(100 - q_1 - q_2)$ and $u_2(q_1, q_2) = q_2(100 - q_1 - q_2)$. Solve for Nash\ equilibrium, and show that their grazing is too much in equilibrium (i.e., tragedy of\ the commons). [5]