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Auction Theory תכנון מכרזים ומכירות פומביות

Auction Theory תכנון מכרזים ומכירות פומביות. Class 1 – introduction. Administration. Instructor: Liad Blumrosen ליעד בלומרוזן blumrosen@huji.ac.il Office hours: Wednesdays 1:30-2:30 Please send an email before you come. Teaching assistant: Assaf Kovo אסף קובו assafkovo@gmail.com

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Auction Theory תכנון מכרזים ומכירות פומביות

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  1. Auction Theoryתכנון מכרזים ומכירות פומביות Class 1 – introduction

  2. Administration • Instructor: LiadBlumrosenליעד בלומרוזן • blumrosen@huji.ac.il • Office hours: Wednesdays 1:30-2:30 • Please send an email before you come. • Teaching assistant:AssafKovoאסף קובו • assafkovo@gmail.com • Course web-page: • http://auctiontheorycourse.wordpress.com/

  3. Requirements • Grading: • 40% - home assignments (about 2 exercises). • 60% - home exam. • Academic integrity: • You can discuss the home assignments, but please write them on your own. • The home exam is done completely on your own without discussing it with anyone. • Participation is mandatory.

  4. Today • Part 1: • Auctions: introduction and examples. • A very brief introduction to game theory. • Part 2: • four simple auctions • Modeling • Strategies, truthfulness. • Efficiency.

  5. Prices • What is the “right” price for objects? • Think about the following case: • But all the values are private: each value is known only to the potential buyers. • You work for the government: how much does the bank worth? • The government wants to sell a big bank. • Buyer 1: willing to pay 200 Billion. • Buyer 2: willing to pay 100 Billion. • Buyer 3: does not need a house, but wants to buy the house if he can resale it with a profit.

  6. Prices • When the preferences of the bidders are known:it is not always clear how to price the objects and how to allocate them. • But we don’t know the preferences… • Buyers will lie and manipulate to get better prices and better allocation. • How can the preferences be revealed?

  7. Auctions

  8. Some examples • Art auctions (Sotheby's) • Sponsored search auctions (Google) • Spectrum Auctions (FCC) • Bond/Stocks issuing

  9. Example 1: English Auctions

  10. Example2: Auctions for Sponsored Search Real (“organic”) search result Ads: “sponsored search”

  11. Example2: Auctions for Sponsored Search

  12. Example2: Auctions for Sponsored Search • An online auction is run for every individual search. • Advertising is effective. • Targeted. • Users in search mode. • (mostly) Pay-per-click auctions. • How ads are sold? We will see later in the course.

  13. Market design and sponsored search • Google’s revenue from sponsored search: Billions of Dollars each quarter. • Every little detail matters. • Advertisers are “selfish” agents: will manipulate the auction if possible. • Complex software development:hard to experiment  theory to the rescue… • Big internet companies (Google, eBay, Microsoft, Yahoo, Facebook, etc.) are hiring well-known economists to design their markets. • Use auction theory.

  14. Example 3: Spectrum Auctions

  15. Example 3: Spectrum Auctions • Federal Communication Commission (FCC) runs auctions for available spectrum since 1994. • Multi-billion dollar auctions. • Also in Europe, Canada, The Pacific, India, etc… • Bidders have complex preferences: • Hard to communicate . • Hard to determine. • Hard to compute the outcome. • One of the main triggers to recent developments in auction theory.

  16. Example 4: bond issues, IPO’s

  17. Why should one learn auction theory? • A widely-used sale tool: • Bonds, rights for natural resources, privatization, procurement, houses, agricultures, equipment, transportation, art, etc… • Popularity grew considerably with the Internet: • Gigantic e-commerce platforms: eBay, amazon. • B2B • Online advertising (search engines, social networks, display advertising). • Simple, well-defined economic environment. • An applicative branch of game theory, information economics. • Popularity  testable ground for theory. • Some beautiful economic theory • implications in different area in economics.

  18. (Estimated) Course outline Part 1: selling a single item • Basic auction formats and concepts. • Efficient auctions, optimal auctions. • Revenue equivalence, the revelation principle, Myerson’s auction. • Extensions to the basic model: • Affiliated types, interdependent types, risk aversion. • Common values, winner’s course. Part 2: multi-unit auctions • Vickrey-Clarke-Groves mechanisms, matching (without money). • Ascending-price auctions • Auctions for unit demand/ substitutes valuations (Demange-Gale-Sotomayor). • Ausubel and Milgrom Auctions • Online advertising and sponsored search. • Digital goods.

  19. Today • Part 1: • Auctions: introduction and examples. • A very brief introduction to game theory. • Part 2: • four simple auctions • Modeling • Strategies, truthfulness. • Efficiency.

  20. Example: Prisoner’s Dilemma • Two suspects for a crime can: • Cooperate (stay silent, deny crime). • If both cooperate, 1 year in jail. • Defect (blame the other). • If both defect, 3 years (reduced since they confessed). • If A defects (blames the other), and B cooperate (silent) then A is free, and B serves a long sentence.

  21. Notation • We will denote a game G between two players (A and B) by G[ SA, SB, UA(a,b), UB(a,b)] where SA = strategies available for player A (ain SA) SB = strategies available for player B (bin SB) UA = utility obtained by player A when particular strategies are chosen UB = utility obtained by player B when particular strategies are chosen

  22. Normal-form game: Example • Example: • Actions:SA = {“C”,”D”}SB = {“C”,”D} • Payoffs:uA(C,C) = -1, uA(C,D) = -5, uA(D,C) = 0, uA(D,D) = -3

  23. A best response: intuition • Can we predict how players behave in a game? • First step, what will players do when they know the strategy of the other players? • Intuitively: players will best-respond to the strategies of their opponents.

  24. A best response: Definition • When player B plays b. A strategy a* is a best response to bif UA(a*,b)  UA(a’,b) for all a’ in SA (given that B plays b, no strategy gains Aa higher payoff than a*)

  25. A best response: example Example:When row player plays Up,what is the best response of the column player?

  26. Dominant Strategies(אסטרטגיות שולטות/דומיננטיות) • Definition: action a* is a dominant strategy for player A if it is a best response to every action b of B. Namely, for every strategy b of B we have: UA(a*,b)  UA(a’,b) for all a’ in SA

  27. Dominant Strategies: in the prisoner’s dilemma • For each player: “Defect” is a best response to both “Cooperate” and “Defect. • Here, “Defect” is a dominant strategy for both players…

  28. Dominant Strategy equilibriumשווי משקל באסטרטגיות שולטות • Definition:(a,b) is a dominant-strategy equilibrium if a is dominant for A and b is dominant for B. • (similar definition for more players) • In the prisoner’s dilemma: (Defect, Defect) is a dominant-strategyequilibrium.

  29. Stability in games • What is the dominant-strategy equilibrium in this game? • None…. • So what would be a “stable” outcome in this game?

  30. Nash Equilibrium • How will players play when dominant-strategy equilibrium does not exist? • We will define a weaker equilibrium concept: Nash equilibrium • Apair of strategies (a*,b*) is defined to be a Nash equilibriumif:a* is player A’s best response to b*, andb* is player B’s best response to a*.

  31. (Pure) Nash Equilibrium • Examples: Note: when column player plays “straight”, then “straight” is no longer a best response to the row player. Here, communication between players help.

  32. Today • Part 1: • Auctions: introduction and examples. • A very brief introduction to game theory. • Part 2: • Four simple auctions • Modeling • Strategies, truthfulness. • Efficiency.

  33. Experiment • כל תלמיד צריך לכתוב לי שתי הצעות מחיר, אחת לכל שיטת מכירה. • ההצעות יכולות, אך לא חייבות, להיות שונות זו מזו. • אפשר להציע 0 אגורות אם לא מעוניינים. • לאחר קבלת הצעות המחיר, אני אטיל מטבע ואבחר באיזו שיטה אני בוחר. שיטה שניה:"שלם את הבא אחריך"ההצעה הגבוהה ביותר זוכה, והתשלום הוא ההצעה השניה הכי גבוהה. • שיטה ראשונה:"שלם את הצעתך"ההצעה הגבוהה ביותר זוכה, והתשלום הוא גובה ההצעה. אם המכירה תהיה "שלם את הצעתך", הצעתי היא 4.31 שקלים אם המכירה תהיה "שלם את הבא אחריך" הצעתי היא 5.11 שלקים לדוגמא:

  34. Why Auction We have an item for sale. Problem:how much bidders are willing to pay? We can ask them… They will probably lie. Auction design: motivate the buyers to reveal their values.

  35. Mechanism design Auction theory is a sub-field of Mechanism Design. We design the market. “Economists as engineers” Design an auction such that in equilibrium we get the results we want.

  36. Goals A seller (“auctioneer”) may have several goals. Most common goals: • Maximize revenue (profit) • Maximize social welfare (efficiency) • Give the item to the buyer that wants it the most. (regardless of payments.) • Fairness:for example, give items to the poor. This is our focus today.

  37. Four auctions We will now present the following auctions. • English Auctions • Dutch Auctions • 1st-price/”pay-your-bid” auctions • 2nd-price/”Vickrey” auctions “Open Cry” auctions “Sealed bid” auctions

  38. English Auctions

  39. English Auctions at ebay

  40. English auction - rules • Price p is announced each time. • At the beginning, p=0. • Raising hand by a buyer: Agreeing to buy the item for p + $1. • If no bidder raised his hand for 1 minute, the item is sold. • To the bidder who made the last offer. • pays his last offer. at $3 p=0 p=1 p=2 p=3 bid=1 bid=3 bid=2

  41. Dutch Auctions Dutch Flower Market

  42. Today

  43. Dutch auction - rules • Price p is announced each time. • At the beginning, p = maximum price. • Seller lowers the price by $1 at each period. • First buyer to raise his hand, wins the items. • Pays current price. at $97 p=100 p=99 p=98 p=97 Me!

  44. Dutch auctions - trivia • One advantage: quick. • Only requires one bid! • US department of treasury sells bonds using Dutch auctions. • The IPO for Google’s stock was done using a variant of a Dutch auction.

  45. Four auctions We will now present the following auctions. • English Auctions • Dutch Auctions • 1st-price/”pay-your-bid” auctions • 2nd-price/Vickrey auctions “Open Cry” auctions “Sealed bid” auctions

  46. 1st -price auctions • Each bidder writes his bid in a sealed envelope. • The seller: • Collects bids • Open envelopes. • Winner: bidder with the highest bid. • Payment: winner pays his bid. Note: bidders do not see the bids of the other bidders. at $8 $5 $8 $5 $3

  47. 2nd -price auctions • Each bidder writes his bid in a sealed envelope. • The seller: • Collects bids • Open envelopes. • Winner: bidder with the highest bid.Payment: winner pays the 2nd highest bid. Note: bidders do not see the bids of the other bidders. at $5 $2 $8 $5 $3

  48. 2nd-price=Vickrey Second-price auctions are also known as Vickrey auctions. Auction defined by William Vickreyin 1961. Won the Nobel prize in economics in 1996. Died shortly before the ceremony… (we will see his name again later in the course…)

  49. Relations between auctions English Auction Dutch auction 1st-price auction 2nd-price auction How do they relate to each other?

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