Question 2 Two bidders are bidding on an item which is auctioned via a first price sealed bid auction. Each bidder's valuation can take one of the three values with the corresponding probabilities: 3 with probability 0.2, 7 with probability 0.4, 9 with probability 0.4. First Nature moves and chooses each bidder's valuation. Then each bidder observes her own valuation, but she doesn't observe the other bidder's valuation. Then bidders simultaneously choose their bids, which have to be a positive integer. A bidder's payoff is 0 if she doesn't win the item. A bidder's payoff is her valuation minus her bid if she wins the item. In case of a tie, a fair coin flip decides the outcome of the auction. a) (10 points) Does the following strategy profile form a symmetric Bayesian Nash equilibrium: Bidder bids 3 if her valuation is 3, bids 7 if her valuation is 7, bids 9 if her valuation is 9. Explain why/why not this is the case. b) (15 points) Does the following strategy profile form a symmetric Bayesian Nash equilibrium: Bidder bids 2 if her valuation is 3, bids 5 if her valuation is 7, bids 6 if her valuation is 9. Explain why/why not this is the case.