Consider an auction with 4 bidders. Their values are given by v1 = 64, v2 = 82,
ID: 1131213 • Letter: C
Question
Consider an auction with 4 bidders. Their values are given by v1 = 64, v2 = 82, v3 = 33 and v4 = 56, respectively. Each bidder knows his own value, but the only thing he knows about the other bidder’s values is that they are a random number drawn equally from the integers {1, ..., 100} and that they are independent from his own value.
(a) Suppose the auctioneer runs an English clock auction. Describe how we expect each bidder to behave, who would win the auction and at what price.
(b) Suppose the auctioneer runs a second-price sealed-bid auction. Describe how we expect each bidder to behave, who would win the auction and at what price.
(c) Now suppose the auctioneer runs a first-price sealed-bid auction. Describe how we expect each bidder to behave. Will the bidder with the highest value necessarily win the auction?
(d) Now suppose the auctioneer runs a Dutch auction. Describe how we expect each bidder to behave. Will the bidder with the highest value necessarily win the auction?
Consider an auction with 4 bidders. Their values are given by ui = 64, v2 = 82, v3 = 33 and a 4-56 respectively. Each bidder knows his own value, but the only thing he knows about the other bidder's values is that they are a random number drawn equally from the integers [1, 100 and that they are independent from his own value. Suppose the auctioneer runs an English clock auction. Describe how we expect each bidder to behave, who would win the auction and at what priceExplanation / Answer
Answer for a)
In English Clock auction Auction starts with low price and players can fetch more information about bids put on the table by other bidders once ruled out of the auction can not come back and resume the bidding , One who remaians at at the ned wins the auction.
For any auction game bidder must match the bid with his valation and this is a dominant nash equillibria strategy they have if they put a bid les than valuation they can incease the chances of winning by raising bid furthur and if they bid more than their valuation then they have a negative payoff at the end and they can reduce it by moving backwards untill they reach to their valuation level hence v = b is NE
Therefore they must reveal their bids equal to their valuation.
b)
In second bid auction game winner with highest bid pays the second bid price while paying for the good.
Even in this auction bidder 1 has to bid >82 to win this auction hence he would pay 82 and net valuation will be (64-82) = -18 which can be minimised if the bid value of bidder 1 moves down to match his valuation and similarly logic can be explained for if he bid less than his valuation
In this case even highet bidder will emerge as a winner
c)
Even in this case Bidder 2 will win the bid as other bidders have no incentive to reduce their bid and they cant increase the bid more than their valuation whic will fetch net negtive payoff to them. Bidder1 with the highest bid has an inentive to lower the bid if every body else lowers it . In first price auction the best response in our case is 3/4 (64, 82, 33, 56) as this game has no dominant strategy the bidder with the highest bid should win this auction.