Lecture 8


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Lecture 8

  1. 1. Auction design
  2. 2. Auctions <ul><li>Often used by governments to privatize public services (electricity, telephone, railways…) or sell the rights for natural resources exploitation (oil) </li></ul><ul><li>Also used at lot on internet (eBay) </li></ul><ul><li>Two types: private value auctions, where each participant has potentially a different value for the good in question (art piece); common value auctions, where the good is worth the same to each participants (oil resources) </li></ul>
  3. 3. Different possible bidding rules <ul><li>English auction: auctioneer starts with a reserve price ; bidders successively offer higher prices; each bid must exceed the previous one by a minimal bid increment. When no participant is willing to increase the bid anymore, the item is awarded to the highest bidder who pays that price. </li></ul><ul><li>Dutch auction: auctioneer starts with a high price and decreases it gradually until someone is ready to buy the item. </li></ul><ul><li>Sealed-bid auction: Each one writes own a bid, and when envelopes are opened, the item goes to the highest bidder who pays the price he offered. Reserve price can exist. </li></ul><ul><li>Vickrey auction: functions like the sealed-bid auction, except that the highest bidder is awarded the item but at the second-highest price </li></ul>
  4. 4. Auction design <ul><li>A single item to be auctioned off. n bidders with private values for the item of v 1 , v 2 , ….. v n , all positive. The seller has a zero value. </li></ul><ul><li>Two objective for the design of the auction mechanism: </li></ul><ul><ul><li>Pareto efficiency: requires that the good be awarded to the person with the highest private value for the good. </li></ul></ul><ul><ul><li>Profit maximization </li></ul></ul><ul><li>If the private values are known to the seller, no difficulty: the seller should sell the good to the person with the highest value and charge that price. </li></ul>
  5. 5. <ul><li>If private values are not known, how to reach these objectives? </li></ul><ul><li>English auction: </li></ul><ul><ul><li>Pareto efficiency is achieved, and the price paid is the second-highest private value + the minimal bid increment. </li></ul></ul><ul><ul><li>Profit maximisation: with a reserve price of zero, not necessarily: </li></ul></ul><ul><ul><li>Ex: two bidders, with values either 10 or 100. 4 possibilities (10,10), (10, 100), (100,10), (100,100). Minimal increment =1 </li></ul></ul><ul><ul><li>Winning bids will be 10, 11, 11 and 100. Expected value to the seller: (10+11+11+100)/4=33. </li></ul></ul><ul><ul><li>If the seller sets a reservation price of 100, he will sell in 3 cases out of 4, hence an expected profit of 75. </li></ul></ul><ul><ul><li>But this is not Pareto efficient since in one case, no one gets the good. </li></ul></ul>
  6. 6. <ul><li>Dutch auction: Here, Pareto efficiency will not be systematically achieved since the outcome depends on the belief of the bidders regarding the private value for other bidders. He the person with the highest private value underestimate the value of the next one, he will wait too long and miss the purchase. </li></ul><ul><li>Same for sealed-bid auction. </li></ul>
  7. 7. <ul><li>Vickrey auction: if everyone bids his true value, the outcome will be pareto efficient. And it is always in each player’s interest to write down their true value. </li></ul><ul><li>Two player, 1 and 2, with value v and bid b. </li></ul><ul><li>The expected payoff for bidder 1 is: </li></ul><ul><ul><li>Prob(b 1 ≥b 2 )[v 1 -b 2 ] </li></ul></ul><ul><li>If v 1 >b 2 , the player 1 wants to make the probability of winning as high as possible, which he can do by setting b 1 =v 1 , </li></ul><ul><li>If v 1 <b 2 , the player 1 wants to make the probability of winning as small as possible which he can do by setting b 1 =v 1 . </li></ul><ul><li>In either case, his best strategy is to bid his true value. </li></ul>
  8. 8. Other auction forms. <ul><li>eBay uses a form of Vickrey auction. It introduced and automated bidding agent. You indicate your maximal value and your initial bid and the proxy bidder increases the bid automatically by the minimal bid increment when necessary. </li></ul><ul><li>Relative to Vickrey auction with sealed id, eBay prompts behaviour of late bidding. </li></ul><ul><li>Escalation auction: the highest bidder wins the item but both the highest bidder and the second highest bidders have to pay the amount they bid </li></ul>
  9. 9. <ul><li>Other example: google ad auction. Position auction: you get on the page in the order of the bids until there is no space left on the page. The highest bidder pays the second bid, the second bidder pays the third etc. </li></ul>