Motivation. A first-price auction (=give the highest bidder the item, then charge them their bid) is a bad idea because, assuming the highest bidder was truthful () then their utility is . Thus this is not DISC and not a good auction. It’s also very hard to reason about. Therefore we have…

def. Second Price Auction. (=Vickery Auction) Give to the highest bidder; charge them the second highest price.

  • An ascending bid auction (=an e-bay auction) is actually a second price auction if you think about it. The last two bidders will increase their bids continually until they reach , and then bidder bids just slightly above () to get the item.
  • ! Not to be confused with Ascending Price Auction; they’re ascending two different things.

thm. Second Price Auction is DSIC.

proof. There are only two cases where a bidder may lie.

  1. Case one: a bidder lies to reduce the price of the item. But does not depend on . Thus this is impossible
  2. Case two: a bidder lies to get the item. But lying to get the item results in negative utility.

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