Bidding Strategy and Auction Design Marc Arthur Kohn
Auctions Auctions entail the transfer of a particular object from a seller to a buyer for a certain price. It is a useful way to sell commodities of undetermined quality. Auctions can be used for single items such as a work of art and for multiple units of a homogeneous item such as gold or Treasury securities. It is the purest of markets: a seller wishes to obtain as much money as possible, and a buyer wants to pay as little as necessary.
Why do we care? • Auctions are a multi-billion dollar business • The US Treasury uses auctions to determine mortgage rates • The FCC uses competitive bidding to allocate licenses for
broadcasting on the electromagnetic spectrum • Stores such as Filene’s Basement use a pricing strategy that reduces the price on items remaining on the racks for longer than a certain time
Auction Formats
First Price Auction – The individual who submits the highest bid wins the auction, and pays that submitted highest bid; can be applied to any type of auction Second Price Auctions – The individual who submits the highest bid wins the auction, and pays the amount submitted by the second highest bidder; can be applied to any type of auction Sealed Bid Auctions – Bids are submitted privately and each bid is evaluated simultaneously; the highest bidder becomes the winner; can be applied to any type of auction Open-outcry Auctions – Bids are submitted openly and publicly for rival bidders to evaluate; the highest bidder becomes the winner; can be applied to any type of auction English Auction – The auctioneer announces a low price and invites ascending bids until no one is willing to go above the last bid made; the last bidder wins Dutch Auction – The auctioneer announces a high price and then announces successively lower bids; the bidder who calls a halt to such announcements first wins the auction
Common-value Auctions – The value of the object is the same for all bidders; each bidder’s estimated valuation vary slightly; also known as “Objective-value” Private-value Auctions – Each bidder places his/her own and unique valuation to the good; for example, valuations can be influenced by sentimental issues and/or imprecise monetary estimates; also known as “Subjective-value” Winner’s Curse – When the winner, and highest bidder, are forced to bid and pay a higher price for the good than its true value (to win) Risk-averse Bidders – A bidder is more concerned about the losses caused by underbidding than the costs associated with bidding at or close to their true valuations; risk-averse bidders want to win without ever overbidding
Which format is the best? The answer depends upon many variables. 1.Seller’s perspective: - tries to reach the highest selling price - decrease incentives to cheat -affiancy (for perisible items)
The Seller’s Choice Before showing why the second-price auction works, we will consider the position of the seller. It’s clear that, by selling the item for the second highest price, the seller is making less profit. In essence, he is buying information (the true valuation of each bidder). However, in the first-price auction, the seller is also making less profit when the bidders shade their bids. The seller must decide which form of auction will reduce his profit less.
Shading Up Suppose you bid higher than your true valuation (b > v) Then if I) (r < v) i.e., the next highest bid is less than your valuation, so you win the item and turn a profit. However, if you had bid (b = v), you wouldâ&#x20AC;&#x2122;ve still won, and wouldâ&#x20AC;&#x2122;ve turned the same profit.
Else if
Shading Up
II) (v < r < b) i.e., the next highest bid is between your valuation and your bid, then you win the item, but you must purchase it for more than your valuation. So, you should’ve bid (b = v); although you would’ve lost the item, you wouldn’t have sustained a loss.
Shading Up Else if III) (b < r) i.e., you do not have the highest bid. If you had bid (b = v), you still wouldâ&#x20AC;&#x2122;ve lost.
1st Summary In cases I and III, bidding (b > v) has the same result as bidding (b = v). In case II, bidding (b > v) is worse than bidding (b = v). So, there is no reason to bid (b > v) instead of (b = v) since 1/3 of the time, the result is worse, and 2/3 of the time, the result is equal.
Shading Down Suppose you bid lower than your true valuation (b < v) Then if I) (r < b) i.e., the next highest bid is less than your bid, so you win the item and turn the profit. However, if you had bid (b = v), you wouldâ&#x20AC;&#x2122;ve still won, and wouldâ&#x20AC;&#x2122;ve turned the same profit.
Else if
Shading Down
II) (b < r < v) i.e., you do not have the highest bid, which is less than your valuation. So, you shouldâ&#x20AC;&#x2122;ve bid (b = v); you wouldâ&#x20AC;&#x2122;ve won the item and turned a profit.
Shading Down Else if III) (v < r) i.e., you do not have the highest bid, which is above your valuation. If you had bid (b = v), you wouldâ&#x20AC;&#x2122;ve still lost.
2nd Summary In cases I and III, bidding (b < v) has the same result as bidding (b = v). In case II, bidding (b < v) is worse than bidding (b = v). Again, there is no reason to bid (b < v) instead of (b = v) since 1/3 of the time, the result is worse, and 2/3 of the time, the result is equal.
Overview So, we have shown that bidding your true valuation is better than both bidding under your valuation and bidding over your valuation. Therefore, it is clear that, in a second-price auction, the best strategy for each bidder is to bid their true valuation. So Vickreyâ&#x20AC;&#x2122;s Truth Serum works