Consider a first-price, sealed-bid auction in which a bidder’s valuation can take one of three values: 5, 7, and 10, occurring with probabilities .2, .5, and .3, respectively. there are two bidders, whose valuations are independently drawn by nature. after each bidder learns her valuation, they simultane- ously choose a bid that is required to be a positive integer. a bidder’s payoff is zero if she loses the auction and is her valuation minus her bid if she wins it. a. determine whether it is a symmetric bne for a bidder to bid 4 when her valuation is 5, 5 when her valuation is 7, and 6 when her valuation is 10. b. determine whether it is a symmetric bne for a bidder to bid 4 when her valuation is 5, 6 when her valuation is 7, and 9 when her valuation is 10.