Problem 1 (20 points). Let d E N be fixed. Consider the class of monomial latency functions of degree d with non-negative coefficients, i.e., Ma = {f : Rzo - Rzo : f(x) = qx, where q 2 0}. Derive a tight bound on the price of anarchy for selfish routing games with latency functions (la)acA E MA. (Hint: The bound of Theorem 1.7 in the Lecture Notes is not tight in this case.)