4. Suppose Players 1 and 2 are participating in a first-price sealed bid auction with private,...

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4. Suppose Players 1 and 2 are participating in a first-price sealed bid auction with private, independent valuations. Each player's valuation of the object to be sold, which is assumed to be worth o to the seller, is drawn from a uniform distribution on [0,1]. Each player knows her own valuation but only the probability distribution on the other player's valuation. Bids are restricted to be in [0,1]. Remember bids are chosen simultaneously, the highest bidder wins and pays the amount of his bid. If two bidders bid the same amount, one of them gets the object with probability 0.5. < (a)(5%) What is a strategy for a player in this game?+ (b)(15%) Bidder 2 decides to choose his bid b2 = .8V2, where v2 is his value. Consider bidder 1 and suppose her value is 0.6. Which is the best bid for her, knowing Bidder 2's bidding function, among these three bids (i) b = .64, (ii) b = .4, (iii) b = .3. Assume she wants to maximize her expected payoff from the auction where she gets .6 - b if she wins and o if she loses, so her expected payoff is given by (.6 - b) Prob(b b2).+ (c)(5%) What would Player 1 bid with three bidders, with Bidders 2 and 3 bidding.8V/2+ and 8V3 respectively? Check for V = .6 and the three bids listed in (b) above.+ 4. Suppose Players 1 and 2 are participating in a first-price sealed bid auction with private, independent valuations. Each player's valuation of the object to be sold, which is assumed to be worth o to the seller, is drawn from a uniform distribution on [0,1]. Each player knows her own valuation but only the probability distribution on the other player's valuation. Bids are restricted to be in [0,1]. Remember bids are chosen simultaneously, the highest bidder wins and pays the amount of his bid. If two bidders bid the same amount, one of them gets the object with probability 0.5. < (a)(5%) What is a strategy for a player in this game?+ (b)(15%) Bidder 2 decides to choose his bid b2 = .8V2, where v2 is his value. Consider bidder 1 and suppose her value is 0.6. Which is the best bid for her, knowing Bidder 2's bidding function, among these three bids (i) b = .64, (ii) b = .4, (iii) b = .3. Assume she wants to maximize her expected payoff from the auction where she gets .6 - b if she wins and o if she loses, so her expected payoff is given by (.6 - b) Prob(b b2).+ (c)(5%) What would Player 1 bid with three bidders, with Bidders 2 and 3 bidding.8V/2+ and 8V3 respectively? Check for V = .6 and the three bids listed in (b) above.+

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