"2. A seller hopes to sell an item, and has two bidders, A and B. The seller knows that the itemis either ideal for A, .ideal for B or ideal for neither. ; The probability of each of the rst two events is z, and there is a I -2z ' - ' probability the object will be ideal for neither. If the item is \"ideal\" for a bidder, the bidder will value winning at 100. Otherwise, a bidder will value Winning at 50. Thetwo bidders can recognize whether an item is ideal for them, and hence know their individual values. ' (a) If the seller runs a second price auction, What is the optimal strategy for each bidder, and the Nash equilibrium? ' (b) What is the expected revenue from the second price auction? (C) Can the publisher raise revenue by setting a reserve (minimum) price? ' By how much? (Hint: it may depend on 2:) ' ((1) Suppose instead that the seller announces that it will rst offer to sell at a price 191;, and then if no one offers to buy at that price, offer 7, , r-a price pL, and that if more than one bidder wants to. buy at a given ' ' .7 7 l'price,,_it will randomize between them in deciding the winner. Find the choices of pH and pL that maximize the seller's revenue, assuming. blddersrfnllynnderstand the mechanism and respond strategically. ~ Cempareltheseller's revenue in (b), (c), and (d). Which is the revs" , uemaXImizmg option for the seller