Problem 14.2 The Generalized Second Price sponsored search auc- tion described in Problem 3.1 induces a payoff-maximization game, where bidder i strives to maximize her utility aj(;(vi - Pj()), where vi is her value-per-click, j(2) is her assigned slot, and P;(i) and a j() Notes, Problems, and Exercises 201 are the price-per-click and click-through rate of this slot. (If i is not assigned a slot, then aj( = Pi(i) = 0.) (a) Assume that each bidder can bid any nonnegative number. Show that even with one slot and two bidders, the POA of PNE can be 0. (b) (H) Now assume that each bidder i always bids a number be- tween 0 and vi. Prove that the POA of CCE is at least