• What is an Action?

    • An auction is a market institution with an explicit set of rules
    • determining ressource allocation and prices
    • on the basis of bids from the market participants

  • Which types of values exist?

    • Independent Private Values (IPV): Each bidder/agent values the good differently. Example: paintings of new artists
    • Common Values: No one knows this true value for sure, but everyone has some guess. These guesses are distributed around the true value. Example: jar with coins, stocks.

  • Which Single Unit Auction Mechanisms do you know? What are there properties/differences?

    • First-price sealed-bid auction:
      • Each bidder submits one sealed (private) bid
      • Highest bidder is allocated the good and pays his bid
    • Vickrey auction:
      • Second price sealed bid auction
      • Highest bidder wins the auction and pays price of second highest bid
      • Weakly dominant strategy: bid the true valuation
    • Dutch auction:
      • Auctioneer announces prices decreasing over time
      • The first bidder who accepts a price is allocated the good for this price
      • Bidder has to decide on how long to wait
    • English auction:
      • The price is successively raised until only one bidder remains
      • Bidding stops when the second last bidder drops out
      • The highest valuation bidder wins and pays price equal to the second highest valuation

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  • Why are first-prise sealed-bid auction and Dutch auction strategically equivalent?

    • Both auctions reveal no information about the other players
    • Find a bid that maximizes the chance of winning while paying as little as possible
    • Bidders do not bid thir true valuation, it would lead to zero profit

  • What are Order Statistics? What can they be used for?

    • Order statistics are the sample values placed in descending order
    • They can be used to calculate the probability that the first or second highest values is less or equal than some value v.
    • They are used to calculate the Sellers Expected Revenue (SER) and Bidders Expected Rents (BER).

  • How is Sellers Expected Revenue (SER) and Bidders Expected Rents (BER) affected by number of bidders?

    • The seller has an advantage: More bidders, more revenue
    • Bidder has a disadvantage: More bidders, more concurents (BER decreases for Independent Private Values and for Common Values)

  • Explain Revenue Equivalence Theorem

    • Under the assumptions of the benchmark model each of the English auction, the Dutch auction, the first-price sealed-bid auction, and the Vickrey auction yields the same price on average → in benchmark model all four auctions have the same price on average
    • This does not imply that the outcomes of the four auction forms are always exactly the same
    • Finding the dominant strategy in an English or Vickrey auction is easy
    • Finding the Nash equilibrium in a first-price sealed-bid auction or Dutch auction is a nontrivial computational problem.

  • Under which assumptions does the hold?

    • A1: the bidders are risk neutral
    • A2: the independent private values assumption applies
    • A3: the bidders are symmetric
    • A4: payment is a function of bids alone,

  • Under which conditions would you choose each auction mechanism covered in this lecture?

    • English, Vickrey: Dominant strategy equilibria; outcome equivalence
    • Dutch, first-price sealed-bid: Nash equilibria, strategic and outcome equivalence