In this problem we will ask how irrational behavior on the part of one bidder affects optimal behavior for the other bidders in an auction. In this auction the seller has one unit of the good which will be sold using a second-price, sealed-bid auction. Assume that there are three bidders who have independent, private values for the good, v1, V2 v3, which are uniformly distributed on the interval [0, 1] (a) Suppose first that all bidders behave rationally; that is they submit optimal bids. Which bidder (in terms of values) wins the auction and how much does this bidder pay (again in terms of the bidder's values)?(b) Suppose now that bidder 3 irrationally bids more than his true value for the object; in particular, bidder 3's bid is (v3 +1)/2. All other bidders know that bidder 3 is irrational in this way, although they do not know bidder 3's actual value for the object. How does this affect the behavior of the other bidders? (c) What effect does bidder 3's irrational behavior have on the expected payoffs of bidder 1? Here the expectation is over the values of v2 and v3 which bidder 1 does not know. You do not need to provide an explicit solution or write a proof for your answer; an intuitive explanation of the effect is fine. [Remember a bidder's payoff is the bidder's value for the object minus the price, if the bidder wins the auction; or 0, if the bidder does not win the auction.]