Optimal Mechanism Design Chapter 16

1. Optimal Mechanism DesignChapter 16 • Organizations develop methods over time to handle allocation problems. Examples of ways to distribute limited products to customers include: • Queuing (waiting in line) for tickets • Estate attorneys divide assets • Auctions to highest bidder • The best way to handle different institutional problems the “optimal mechanism design” 2005 South-Western Publishing

2. What is the best way to divide a deceased individual’s estate? What mechanism will encourage open communication and a fair division? These are the types of issues discussed in finding an optimal design. Fair division of a decaying prize Suppose the division of an award between two parties shrinks each time one party refuses the agreement. An incentive is created to agree to a 50:50 split; otherwise, the prize may get smaller. An Optimal Design Mechanism

3. Dissolution of Assets in a Partnership {$1.9 m, $1.1 m.} Accepts {$1 m, $1 m.} • The payoffs decay as illustrated in Figure 16.1 on page 716. • A $3 million dollar partnership is dissolved. Joanne’s payoff given first in each pair, and Kathy’s is given second. • A the negotiation continues, each party loses out to attorneys fees. • Kathy can see all the way out to the end-game, she is best off taking the first (unequal) split to receive $1.1 million. • Using her right of refusal will lead only to lower payoffs for Kathy. Kathy I Accepts Joanne 1 offers to give $1.1 m to Kathy Rejects Joanne II Kathy II offers $1 to Joanne Rejects Etc.

4. The Service Queue Problem:customers wait in line • First-come, first-served The people with the lowest cost of time get the tickets. • Last-come, first-served removes the incentive to wait in line. The best strategy is to show up anytime, whenever the ticket window is open. • Stratified lotteries advanced reservation tickets are assigned different prices than last minute walk-ups.

5. Types of Auctions • In English auctions, the prices rise as more bids arrive. • Used by ‘auctioneers’ to ask for higher and higher bids • In Dutch auctions, a high price is announced, and if no one agrees, the auctioneer lowers the price until the first bid arrives. • If mineral rights to 1,000 acres of land were auctioned, the winning bid may elect to purchase less than 1,000 acres or rights. • For-sale-by-owner sellers of homes keep lowering price until they find a buyer. • Reservation price the minimum acceptable bid. (A reserve) • eBay uses reservation prices to prevent the sale of an item at a mere $1.

6. Simultaneous bidding open outcry at estate auctions. Information about other bidders valuation is revealed price discovery occurs used by Priceline with Dutch descending prices Sequential bidding such as private placement for newly issued securities. used by eBay with English ascending prices Bidding rules can require minimum increases in prices eBay requires each bid to be at least $1 higher than the prior bid. Auction Design and Information Economics

7. Bid prices can be discrete or continuous by agreed increments, as in 1/8 or 1/16 for stocks in the past or any decimal price now. • By January 29, all stocks on the NYSE and AMEX traded to the penny, rather than in fractional prices. • Bids can be sealed or posted sealed bids make them anonymous and secret to other bidders; whereas posted means all see the bid. • Bids can be one-time-only or multiple rounds.

8. Do I hear $100? Distribution of Values Value • Draw a distribution on its side, with those having the highest value at the top • If the auction is for one item, say a Ming vase, in an English auction the highest bidder is the winner • If the Ming vase is sold at a Dutch auction, in theory the price starts high and descends. The winner is also the highest bidder. • In theory and practice the two are nearly identical for risk neutral bidders • The winner has the highest value, but notice that the “expected value” is lower • That difference is part of the winner’s curse Winner’s Price expected value Freq

9. Winner’s Curse • If the true value of an item is not known, but bidders have a distribution of values that they are willing to pay, the winning bid is very likely to be higher than the true value. • The regret for the bidder is that he or she paid too much: the winner’s curse. • If everyone is aware of the winner’s curse, then all would bid less than what they think is its true value. This problem has led some auctions to award the highest bidder with the second-best price in a sealed bid auction. Even when you win, the price will be lower than what you bid, so you bid more.

10. Information Revealed in Common-Value Auctions • Common-value auctions are ones where the bidders have identical valuation of the item when information is complete (as in a CD from Nora Jones or John Mayer) • Silent auction, where each writes a price higher than the last works well for these types of items • For simultaneous sealed-bid auctions, the bidder offers prices below their expected value. • No information is conveyed to competitors. • For simultaneous, open-bidding auctions, information is revealed by the bids of others. • One variation is multiple rounds. • Bidding for broadcast spectrum bidding, the FCC used 112 rounds over a four-month bidding period.

11. Strategy with Open Bidding Design • Each bidder tries to elicit sufficient information to identify the value of the item bid upon • Example: Bidding to buy bandwidth • After the sealed bids are open, the winner many have bid strategically low to avoid the winner’s curse. • Buy having a second (and third) round, the winning price from the first round is known. • Bidding in the next round “updates” information to include the winning price (part of Bayesian information updating) • The winning bid in the final round comes closer to the true value with this approach

12. Private-value auctions are where bidders have different valuations for the item (e.g., vintage postage stamps) The highest value bidders may wish to wait-and-see in English open outcry auctions. In sealed-bid auctions, this strategy does not work. Even with sealed bidding, the fear of the winners curse may lead to underbidding. A Vickery auction is the second-highest sealed bid auctions. Second-highest sealed bids are used to reduce underbidding. Knowing that you pay less than bid helps to move bid closer to one’s private value. As the number of bidders rises, underbidding tends to decline. Vickery shows the optimal underbidding is 1/Nth the true value, with N the number of bidders. Strategic Underbiddingin Private-Value Auctions

13. eBay and Internet auctions • www.ebay.com- operates the leading online trading community in which buyers and sellers are brought together in an auction format to trade personal items such as antiques, coins, collectibles, computers, memorabilia, stamps and toys. • What type of auction is it? (English or Dutch?) • Why is there a reservation price?

14. Revenue Equivalence of Auction Types • Experiments confirm the following • For common-value auctions: • For risk-neutral bidder, the rank order is: English > second highest sealed bid > Dutch = highest price sealed bid • The seller does better with English auctions, whether risk neutral or not. • For private-value auctions: • For risk neutral bidders, English, Dutch, highest sealed bid, or second highest bid auctions are all alike in their outcome. • When bidders are risk-averse,the rank order from highest is: Dutch = highest price sealed bid > English = second highest sealed bid

15. Dutch Auction IPOs • Google went public in in a so-called Dutch auction IPO • Stock prices are likely to be viewed a private-value auctions • The highest price to the firm from risk-averse investors would come a Dutch auction, although purists would call it a modified Vickery auction. • The price is not the second highest price, but the price that clears the market • Since winning bidders are taken in descending order, it is somewhat like a Dutch auction.

16. IPO Auction(A Modified Vickery Auction) • All bidders submit the number of shares that they would like to buy and the maximum price that they are willing to pay for each of those shares. • When all bids are in, they are opened and sorted into descending order by price • A running total of shares requested is calculated. • The market clearing price is the price at which the running total of shares requested equals the number of shares offered. • All bidders who bid at or more than the market clearing price receive the shares that they requested • They all pay the market clearing price (which will always be less than or equal to their maximum bid price).

17. Example of a Modified Vickery Auction • Suppose that 1,000 shares are offered for sale and five bids were submitted: Listed in Descending Order of Price   Bidder A 300 shares @ $100 each 300 running total Bidder B 300 shares @ $ 80 each 600 running total Bidder C 200 shares @ $ 75 each 800 running total Bidder D 300 shares @ $ 70 each 1,100 running total Bidder E 200 shares @ $ 50 each 1,300 running total • Then Bidders A, B and C would get the shares that they requested • Bidder D would get 200 of the 300 that he requested. • All four bidders would pay $70 for each share regardless of the fact that some bidders were prepared to pay more. • The IPO brings in $70,000.

18. Cost Revelation in Joint Ventures and Partnerships • Potential partners have different information upon beginning a venture together, with each partner claiming higher costs for their share than their true costs. • Some joint ventures never occur because of this behavior, even though both would benefit from the venture. • Contractual ways to deal with asymmetric information include: • offer independent appraisals of the product. • offer warrantees as a signal of a good product. • offer leases with a high residual value. • offer a contingent payment if anything is amiss in the deal. • The Clarke-Groves mechanism creates incentives for partners to reveal the true costs. a. The mechanism is to assign probabilities to the revelation of costs of the partner. b. After the other partner's expected costs are covered, they receive the residual or net profit. c. Then each has an incentive to reveal their true cost.

19. Optimal Incentives Contract • An agreement about the payoffs and penalties which creates appropriate incentives is called an optimal incentives contract. • The penalty is often the termination of a contractual relationship. A breach of a contract leads to termination of the contract. • If the contract creates a stream of profits, then a breach is a costly penalty. • The most common example: an employee who steals is fired! • If the employee felt the employment at that firm was rewarding, the penalty of firing is severe.