questions are in file attached
Tutorial5 TutorialforLectures5 1) Consider an auction with n bidders. Assume that vi is the valuation of bidder i and bi is the bid price of bidder i. Assume that no two bidders’ bidding prices are same. For each type of auctions: English auction, Dutch auction, first-price sealed-bid auction and second-price sealed-bid auction, what is the utility (payoff) of each bidder. 2) Assume that a market received the following shouts: Selling (asks): 95, 113, 122, 108, 103, 98 Buying (bids): 97, 99, 95, 110 1) If the market uses Equilibrium Matching, what are the matches it can produce? _______________________________________________ If the market uses Maximum Matching, what are the matches it can produce? _______________________________________________ 2) What is the social welfare of the transactions under each matching policy? If the market uses Equilibrium Matching: ____________________________ If the market uses Maximum Matching: ______________________________ 3) Use 4 heap matching algorithm to recalculate equilibrium matches. Draw the final four heaps (four trees), marked with Sout, Sin, Bin and Bout respectively. 4) If the market applies Discriminatory Pricing Policy with k=0.6, what is the clearing price for each match in the equilibrium matching? _______________________________________________ 5) If the market applies Fixed Charging Policy with the rate as follow: Shout fee: $2 per shout Transaction fee: $1 per shout Profit fee: 15% After all the shouts listed and all the matched shouts are transacted, how much the market can collect from this period of trading for each matching policy? 3. Consider a scenario of AD auction with quality score. There are five advisers (#1 - #5) who bid for listing at $12, $8, $5, $5 and $1 per click. The quality scores of their websites are 5, 20, 7, 2 and 6, respectively. Only three positions will be available. Which advisers’ websites will be listed in which order? What is the actual CPC they need to pay, respectively?