2. Three bidders: Dennis, Betsy, and Michael are Private Valuations bidding for two items: X and Y. The bidders' +Bidder X Y X&Y (non-additive) private valuations for the items are Dennis 6 4 12 given to the right. The seller decides to hold three Betsy 7 8 simultaneous sealed-bid auctions: X and Y are Michael 5 7 sold separately in second-price auctions and the bundle X&Y is sold in a first-price auction. The items are sold as a bundle if the high bid for X&Y meets or exceeds the sum of the separate prices for X and Y. Dennis' bid is given by bo, Betsy's by be and Michael's by bM. Suppose that the bidding for X is bo = 6; be = 7 and bM = 1. The bidding for Y is bD =4; bB = 1 and bM = 5; and the bidding for bundle X&Y is bo = 8; be = 7 and bM = 6. Your answers to the questions below do not require the construction of a game box. Do not make any assumptions about the distribution of valuations. a. Given these bids who wins the item(s) and at what price(s)? b. Is this collection of bids a Nash equilibrium? Why or why not