1. (20pts) Christie's is auctioning off Banksy's "Game Changer". There are two bidders: Hande and Yamur.A bidder's valuation of the painting is 5 with probability 0.2, 8 with probability 0.5, or 11 with probability 0.3. Valuations are private information. Suppose the rulesof the auction are as follows: -The auction is a first price sealed bid auction.-Bids must be positive integers.-If the bidders submit the same bid then the auctioneer flips a coin to determine the winner.(a)(10 pts) Determine whether it is a symmetricBayes-Nash equilibrium for a bidder to bid 4 when her valuation is 5, 6 when her valuation is 8, and 8 when her valuation is 11. Defend your answer carefully.(b)(10pts) Determine whether it is a symmetric Bayes-Nash equilibrium for a bidder to bid 4 when her valuation is 5, 7 when her valuation is 8, and 10 when her valuation is 11. Defend your answer carefully.