Optimal Mechanism Design Finance 510: Microeconomic Analysis.

Slides:



Advertisements
Similar presentations
Yossi Sheffi Mass Inst of Tech Cambridge, MA ESD.260J/1.260J/15.
Advertisements

(Single-item) auctions Vincent Conitzer v() = $5 v() = $3.
Network Economics -- Lecture 4: Auctions and applications Patrick Loiseau EURECOM Fall 2012.
Private Information and Auctions. Auction Situations Private Value – Everybody knows their own value for the object – Nobody knows other peoples values.
CPS Bayesian games and their use in auctions Vincent Conitzer
Economics 100B u Instructor: Ted Bergstrom u T.A. Oddgeir Ottesen u Syllabus online at (Class pages) Or at
1 Auctioning Many Similar Items Lawrence Ausubel and Peter Cramton Department of Economics University of Maryland.
Auctions. Strategic Situation You are bidding for an object in an auction. The object has a value to you of $20. How much should you bid? Depends on auction.
Chapter 25: Auctions and Auction Markets 1 Auctions and Auction Markets.
Intermediate Microeconomics Midterm (50%) (4/27) Final (50%) (6/22) Term grades based on relative ranking. Mon 1:30-2:00 ( 社科 757)
Bidding Strategy and Auction Design Josh Ruffin, Dennis Langer, Kevin Hyland and Emmet Ferriter.
Auctions Auction types: –First price, sealed bid auction –Second price, sealed bid auction –English auction (ascending bid auction) –Dutch auction (descending.
Econ 805 Advanced Micro Theory 1 Dan Quint Fall 2007 Lecture 2 – Sept
Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill Companies, Inc., 1999 Managerial Economics & Business Strategy Chapter.
Game Theory in Wireless and Communication Networks: Theory, Models, and Applications Lecture 6 Auction Theory Zhu Han, Dusit Niyato, Walid Saad, Tamer.
Game Theory “A cynic knows the price of everything and the value of nothing” - Oscar Wilde, Lady Windemere’s Fan Mike Shor Lecture 11.
Welcome Auctions Jonathan D. Wareham
Auctions An auction is a mechanism for trading items by means of bidding. Dates back to 500 BC where Babylonians auctioned of women as wives. Position.
1 Chapter 6: Auctions SCIT1003 Chapter 6: Auctions Prof. Tsang.
Federal Communications Commission NSMA Spectrum Management Conference May 20, 2008 Market Based Forces and the Radio Spectrum By Mark Bykowsky, Kenneth.
Auctions Julina, Hales, Lauren, and Jaki. Definitions Auction: a process of buying and selling goods through bids for an optimal price. Auctions must.
Auction. Types of Auction  Open outcry English (ascending) auction Dutch (descending) auction  Sealed bid First-price Second-price (Vickrey)  Equivalence.
Private-value auctions: theory and experimental evidence (Part I) Nikos Nikiforakis The University of Melbourne.
Do software agents know what they talk about? Agents and Ontology dr. Patrick De Causmaecker, Nottingham, March
Auctions Ruth Tarrant. Classifying auctions What is the nature of the good being auctioned? What are the rules of bidding? Private value auction Common.
The Economics of Information
Liz DiMascio Paige Warren- Shriner Mitch Justus DUTCH AND ENGLISH AUCTIONS IN RELATION TO THE TULIP MARKET.
Slide 1  2002 South-Western Publishing Coordination and control are problems for all business organizations. The larger the organization, the larger the.
Auction. Definition An auction is a process of buying and selling goods or services by offering them up for bid, taking bids, and then selling the item.
Introduction to Game Theory
Auctions. An auction is a process of buying and selling goods or services by offering them up for bid ( The price at which a buyer is willing to close.
1 Teck-Hua Ho April 18, 2006 Auction Design I. Economic and Behavioral Foundations of Pricing II. Innovative Pricing Concepts and Tools III. Internet Pricing.
Chapter Seventeen Auctions. Who Uses Auctions? u Owners of art, cars, stamps, machines, mineral rights etc. u Q: Why auction? u A: Because many markets.
1 Teck-Hua Ho April 22, 2006 Auction Design I. Economic and Behavioral Foundations of Pricing II. Innovative Pricing Concepts and Tools III. Internet Pricing.
Auctions and dynamic pricing. When is the auction mechanism useful? We do not know the true value of the good or service on offer We do not know the true.
Auctions Hal R. Varian. Auctions Auctions are very useful mean of price discovery eBay: everyone’s favorite example DoveBid: high value asset sales at.
Managerial Economics & Business Strategy
and Lecture Notes in Game Theory1 Game Theory Applications: Lecture Notes Course Website u Galina.
This Week’s Topics  Review Class Concepts -Sequential Games -Simultaneous Games -Bertrand Trap -Auctions  Review Homework  Practice Problems.
This Week’s Topics  Review Class Concepts -Auctions, continued -Repeated Games -Bertrand Trap & Anti-Trust -Auctions.
Auctions Yunon Chuang. What are auctions? n Auction Markets: –traders transact directly against the orders of other traders by communication through a.
Chapter 19 Equivalence Types of Auctions Strategic Equivalence
Strategic Demand Reduction in homogenous multiunit auctions (where bidders may be interested in more than one unit)
Introduction to Auctions David M. Pennock. Auctions: yesterday Going once, … going twice,...
Introduction to Game Theory
Auction Seminar Optimal Mechanism Presentation by: Alon Resler Supervised by: Amos Fiat.
Combinatorial Auctions By: Shai Roitman
Session 8 University of Southern California ISE544 June 18, 2009 Geza P. Bottlik Page 1 Outline Two party distributive negotiations (Win/Lose) –Case history.
Games People Play. 12: Auctions Games People Play. Auctions In this section we shall learn How different types of auctions allocate goods How to buy.
Auctions and Bidding. 2 Auction Theory Auction theory is important for practical reason empirical reason –testing-ground for economic theory, especially.
4. The Theories and the Real World. Strategic Behavior in Business and Econ Outline 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game.
Auctions Shyam Sunder, Yale University Kozminski Academy Warsaw, June 22, 2013.
Auctions An auction is a mechanism for trading items by means of bidding. Dates back to 500 BC where Babylonians auctioned of women as wives. Position.
Economics 434 Financial Markets Professor Burton University of Virginia Fall 2015 Fall, 2015.
Auctions serve the dual purpose of eliciting preferences and allocating resources between competing uses. A less fundamental but more practical reason.
Auctions serve the dual purpose of eliciting preferences and allocating resources between competing uses. A less fundamental but more practical reason.
Auctions Great Lakes Institute of Management, Chennai March 4, 2012.
6-1 Economics: Theory Through Applications. 6-2 This work is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
Incomplete Information and Bayes-Nash Equilibrium.
Advanced Subjects in GT Prepared by Rina Talisman Introduction Revenue Equivalence The Optimal Auction (Myerson 1981) Auctions.
Lecture 4 on Auctions Multiunit Auctions We begin this lecture by comparing auctions with monopolies. We then discuss different pricing schemes for selling.
1 Types of Auctions English auction –ascending-price, open-outcry Dutch auction –descending-price, open-outcry 1 st price sealed bid auction –known as.
Bayesian games and their use in auctions
Shyam Sunder, Yale University Kozminski Academy Warsaw, June 23, 2012
Tuomas Sandholm Computer Science Department Carnegie Mellon University
Auctions: Basic Theory & Applications
Auctions An auction is a mechanism for trading items by means of bidding. Dates back to 500 BC where Babylonians auctioned of women as wives. Position.
CPS Bayesian games and their use in auctions
Presentation transcript:

Optimal Mechanism Design Finance 510: Microeconomic Analysis

Optimal mechanism design deals with institutional rules chosen to serve some explicit optimization goal. Example Suppose that your learn of a long lost uncle that has died and has left you and your sister $3M. You and your sister need to decide how to split the $3M. However, the lawyers fees are $1M per negotiating round. You and your sister agree to the following:  Coin flip decides who will make the first offer  Offers are made in $100,000 increments  Once an offer is made, the other has the right of refusal  No communication allowed during settlement

You Sister Offer AcceptReject Sister Offer You AcceptReject You Offer Sister AcceptReject ($0,$0) Round 1 Round 2 Round 3 With $1M left to split, you offer your sister $100,000 (Which is strictly preferred to $0)

You Sister Offer AcceptReject Sister Offer You AcceptReject You Offer Sister AcceptReject ($0,$0) Round 1 Round 2 Round 3 With $2M left to split, your sister offers $1,000,000 (Which is strictly preferred by you to $900,000) You: $900,000 Sister: $100,000

You Sister Offer AcceptReject Sister Offer You AcceptReject You Offer Sister AcceptReject ($0,$0) Round 1 Round 2 Round 3 With $3M left to split, you offer your sister $1,100,000 (Which is strictly preferred to $1,000,000) You: $900,000 Sister: $100,000 You: $1,000,000 Sister: $1,000,000 You: $1,900,000 Sister: $1,100,000

Optimal mechanism design deals with institutional rules chosen to serve some explicit optimization goal. We initially had the following rules:  Coin flip decides who will make the first offer  Offers are made in $100,000 increments  Once an offer is made, the other has the right of refusal  No communication allowed during settlement Suppose that we drop the last rule (no communication) and as a result, you sister is able to convince you that she only cares about what she gets relative to you! i.e. ($0, $0) is preferred to ($600,000, $400,000)

You Sister Offer AcceptReject Sister Offer You AcceptReject You Offer Sister AcceptReject ($0,$0) Round 1 Round 2 Round 3 With $1M left to split, you offer You: $400,000 Sister: $600,000

You Sister Offer AcceptReject Sister Offer You AcceptReject You Offer Sister AcceptReject ($0,$0) Round 1 Round 2 Round 3 With $2M left to split, your sister offers $500,000 (Which is strictly preferred by you to $400,000) You: $400,000 Sister: $600,000

You Sister Offer AcceptReject Sister Offer You AcceptReject You Offer Sister AcceptReject ($0,$0) Round 1 Round 2 Round 3 You: $400,000 Sister: $600,000 You: $500,000 Sister: $1,500,000 With $3M left to split, you offer You: $700,000 Sister: $2,300, to one 3 to one

Optimal mechanism design deals with institutional rules chosen to serve some explicit optimization goal. No CommunicationCommunication You: $1,900,000 Sister: $1,100,000 You: $700,000 Sister: $2,300,000 If you were designing the rules of the negotiation process, which would you choose?

It is customary for the goods or services to be handed out on a first come first serve basis. Therefore, if a line forms, the newest arrival goes to the end of the line. Could this mechanism be improved on? With Last Come First Serve  Lines disappear  Goods/services are distributed to those with the highest value (no lines)  Individuals need not alter their schedules With First Come First Serve  Lines are unnecessarily long  Goods/services aren’t necessarily distributed to those with the highest value  Individuals inefficiently alter their schedules to avoid the line

Auction Design In 2000, revenues from online auctions was $6.5 Billion. In 2003, that number grew to $30 Billion!! Experts expect revenues in 2006 to exceed $50 Billion! Auctions have been used for: The Babylonians used auctions to arrange marriages The Greeks used auctions to award mineral rights The French utilized a “candle auction”. Bids were accepted until the candle burned out (similar to EBay's timed auctions) The Dutch used auctions to sell tulips (creating the Dutch auction) T-Bills are sold by the US Treasury via auction The NYSE is an auction market

Auctions are distinguished by their rules Sequential: There are always re-bid opportunities Simultaneous: Each player gets one bid Minimum Improvement: There exists a minimum “unit” for bidding Continuous: No minimum “unit” Minimum Improvement: There exists a minimum “unit” for bidding Continuous: No minimum “unit” Bids can be sealed (private), open outcry, or posted anonymously Some auctions have a minimum allowable bid (reserve price)

Who Pays and How Much? All Bidders Pay: Anyone with an “acceptable” bid pays and gets the product First Price Auction: Highest Bid wins and pays his/her bid Nth Price Auction: Highest Bid wins and pays the amount of the Nth highest bid English Auctions: Open outcry auction. Last bidder (with the highest offer) wins (ascending auction) Dutch Auctions: The first bidder to accept wins as the auctioneer reads off descending prices (descending auction) Does Auction Type Matter?

Sequential Minimum Bid Improvement Posted Prices Multiple Rounds Open Bidding Reserve Price First Price English Ascending Price Seller is Known Simultaneous Continuous Posted Prices (Reverse Auction) One Time (If Seller “Hits”) Credit Card Immediately Authorized No Reserve All Acceptable Bids Pay Dutch Auction Seller is Anonymous VS

Suppose that you are bidding on an object of unknown value to you (but known to the seller). You know its worth between $0 and $100 to the seller and you also know that your value is 50% above the seller’s. What should your bidding strategy be? Consider an example with three possible values: $100, $55, and $0 BID $0 $55 $100 All Offers Refused V = $100 V = $55 V = $0 V = $55 V = $100 A ( $-55, $55) A ($27.50, $0) A ( $95, -$45) A ( -$100, $100) A (-$17.50, $45) A ($50, $0) R ( $0, $0)

The Winner’s Curse BID = $0 All offers rejected Expected Gain = $0 BID = $55 Accepted only if V = $0 Expected Gain = -$18 BID = $100 Accepted if V = $100 or V = $55 Expected Gain = -$39 The Best Strategy is to bid $0!! (the expected value is $51) The Winner’s curse states that in an Auction with asymmetric information, if you win the auction, you have definitely overpaid! Bidders are aware of the winner’s curse. Therefore, there is an incentive to underbid (or not bid at all)

The Winner’s Curse Bids for Offshore Oil Contracts (in Millions of 1969 Dollars) Santa Barbara Channel $43.5$32.1$18.1$10.2$6.3 Alaska North Slope $10.5$5.2$2.1$1.4$.5 Bids for FCC Spectrum Rights (in Millions of 1995 Dollars) Miami Metro Area $131.7$126.0$125.0$119.4$119.3 Dallas Metro Area $84.2$72.0$ Source: R. Weber, “Making More For Less”, Journal of Economics and Management Strategy, Fall 1997

Open bidding allows bidders to react to information revealed in prior rounds. The FCC used open bidding when they recently auctioned broadband PCS MarketPopulationWinnerSecondBidPrice/Pop New York26.4MWirelessAlaacr$442.7$16.76 San Francisco11.9MPacTelAmerPort$202.2$17.00 Charlotte9.8MBellSouthCCI$70.9$7.27 Dallas9.7MWirelessGTE$84.2$8.68 Houston5.2MPrimeCoWireless$82.7$15.93 New Orleans4.9MPrimeCoPowertel$89.5$18.17 Louisville3.6MWirelessPrimeCo$46.6$13.10 Salt Lake City2.6MWirelessGTE$46.2$17.95 Jacksonville2.3MPrimeCoGTE$44.5$19.56 Source: P. Crampton, “The FCC Spectrum Auctions”, Journal of Economics and Management Strategy, Fall 1997

Suppose that the value of the Louisville, Kentucky market is a random variable with 6 equally likely possibilities: $10, $20, $30, $40, $50, $60 (Expected Value = $35) You are competing with one other bidder with the same priors (beliefs about the market value). - common value, common information Oral English Auction Your Bid: <$35 Competitor’s Bid: <$35 Sealed Bid Auction Your Bid: <$35 Competitor’s Bid: <$35 The open auction yields no benefits over the sealed bid auction because there is no information to reveal.

Now, suppose that you and your competitor have the same values, but different information about the distribution - common value, private information Sealed Bid Auction Your Bid: <$40 Competitor’s Bid: <$33 You: $20, $40, $60 (each with the same probability) Opponent: $10, $40, $60 (each with the same probability) Expected Value = $40 Expected Value = $33.67 You should win the auction and pay less than $40

Now, suppose that you and your competitor have the same values, but different information about the distribution - common value, private information You: $20, $40, $60 (each with the same probability) Opponent: $10, $40, $60 (each with the same probability) Expected Value = $40 Expected Value = $33.67 Oral English Auction: Round 1 Your Bid: <$40 Competitor’s Bid: <$34 Both parties learn that $10, $20, $30, and $50 are not possibilities (you eliminated $10, $30, and $50 while your opponent eliminated $20,$30, and $50) Oral English Auction: Round 1 Your Bid: <$50 Competitor’s Bid: <$50 Both bids in round 2 are more informed!!

Private Value Auctions In private value settings, each bidder has the same information, but a places a different value on the object (e.g. fine art). In this setting, those with high valuation prefer not to reveal themselves and, hence, would underbid in an open outcry auction Suppose that there are two bidders for an object. (A and B). Both believe the value of the object to be between $0 and $10M (with a uniform distribution). Bidder A places valueon the object Bidder A places valueon the object Both are following strategies of bidding an amount equal to some fraction of their true value

Bidder A places valueon the object Bidder A places valueon the object Both are following strategies of bidding an amount equal to some fraction of their true value Bidder A wins if

10M 1

Optimal Bidding by Player A First Order Necessary Conditions

Bidder A places valueon the object Bidder A places valueon the object Both are following strategies of bidding an amount equal to some fraction of their true value The Nash equilibrium of this game is for both bidders to submit a bid equal to ½ of their private values. With to bidders, optimal strategy is to underbid by 50%!!!

-50% -20% -10% 2510 Number if Bidders It can be shown that with N bidders, the optimal strategy is With Private Value auctions, it pays to have a lot of bidders (as the number if bidders gets arbitrarily large, everyone bids their true value!)

Alternatively, we could deal with the underbidding problem by holding a second price auction In this setup, the highest bidder wins, but pays the amount equal to the second highest bid Lets repeat the previous example, but with a second price auction

Is there any incentive to bid higher than your private valuation? No. By raising your bid, you increase your odds of winning, but you face the possibility of paying more than you private value! Is there any incentive to bid lower than your private valuation? No. Lowering your bid has no impact on your purchase price, but lowers you odds of winning. Second price auctions avoid underbidding as well as the winner’s curse by giving bidders the incentive to reveal their values (incentive compatibility)

Do All Auctions Yield the Same (Expected) Revenues? Dutch Auctions = 1 st Price Auctions (sealed bid) As the price falls, the individual with the highest value will be the first to speak. He/She will win, and pay an amount equal to his/her bid English Auctions = 2 nd Price Auctions (sealed bid) As the price rises, the individual with the highest value will be the last to bid and will offer an amount just slightly higher than the previous bidder. 1 st Price Auctions (sealed bid) vs. 2 nd Price Auctions (sealed bid)?? In first price auctions, the high bid is paid, but everybody has the strategy of underbidding.

Revenue Equivalence Private ValuesCommon Values Risk Neutral 1 st Price = 2 nd Price1 st Price < 2 nd Price Risk Averse 1 st Price > 2 nd Price1 st Price ?? 2 nd Price It turns out that you can rake the expected returns from different auction rules. The two important questions are Are valuations privately or commonly held? Are bidders risk neutral or risk averse?

Revenue Equivalence Private Values (More Asymmetric Information) Common Values (Less Asymmetric Information) Risk Neutral 1 st Price = 2 nd Price1 st Price < 2 nd Price Risk Averse1 st Price > 2 nd Price1 st Price ?? 2 nd Price Consider the following Products. If you were the seller, which auction type would you prefer? Treasury Bills? IPOs? Artwork? Logging Rights? The type of auction you choose depends on the environment you face!!