Leticia Saldain Guadalupe Segura

1. The design of successfulon-line auctions Leticia Saldain Guadalupe Segura

2. Outline • E-bay basics • Reputation Mechanisms • Low-valued items vs. high-valued items • Pennies: US Cent and Indian Head • Paul Reed Smith Guitar • Last-minute bidding

3. E-Bay basics • On-line auctions started in 1995 • 1998: e-bay had > 3 billion transactions • Growth rate > 10% per month • Over 3 million individual auctions / week • 7 million unique individuals visit site / month • Over 2000 unique categories

5. E-bay auction • Second price auction • Ascending-bid (English) format - fixed time and date • Reservation price • Auction lasts 3-10 days • “proxy bidding” system (Vickrey auction) • Seller chooses • Opening bid amount • Secret “reserve price” • Length of auction • Sellers pays two fees: non-refundable insertion fee and final value fee • E-bay takes no risk

6. Reputation Mechanisms Analyzing the Economic Efficiency of eBay-like Online Reputation Reporting Mechanisms By Chrysanthos Dellarocas

7. Effects of reputation • Studied by Economists • Little attention to the mechanisms for forming/communicating reputation • computer scientists have focused on design/implementation of reputations systems

8. On-line Reputation Reporting Systems Goal: to induce good behavior in markets with asymmetric information • Feedback profile = reputation • Quality signal and control Allows a market to exist!

9. Market for Lemons (Akerlof 1970) Example: consider 9 used cars Quality levels: 0, ¼, ½, ¾, 1, 1 ¼, 1 ½, 1 ¾, 2 Assume cardinality (e.g. car with value 1 has twice the quality of car with value ½) Assumptions: • quality of car known to seller • buyer only knows the distribution of quality • seller: reserve value = 1000*q • buyer: reserve value = 1500*q

10. Market for Lemons (cont’) cars sold in an auction: • Initial price $2000/car (all owners are willing to sell their car) • Buyers : average quality = 1, bid <= 1500 Auctioneer must reduce price to 1500: • at this price seller 8 and 9 (best two cars) will withdraw from market (why?) • average quality of remaining cars fall (q = ¾) • buyers are only willing to pay $1125 (1500* ¾ ) Auctioneer must try a lower price…and so on NO EQUILIBRIUM SATISFYING BOTH BUYERS AND SELLERS IS FOUND!

11. Conclusions: • When potential buyers only know the average quality of used cars, market prices will be lower than the true value of top-quality cars • Owners of top-quality cars will withhold cars from sale GOOD CARS ARE DRIVEN OUT OF MARKET BY LEMONS! • Cars will not be sold even though potential buyers value the cars more than current owners Result from asymmetric information!

12. E-Bay Marketplace • Asymmetric information • Incentive for seller to over-estimate quality and increase profits • Need to provide information to buyers Reputation Mechanisms allow market to exist by reducing asymmetric information!

13. Model to analyze efficiency of binary RM Assumptions: • real quality (qr) is unknown to buyer • buyer prefers high quality to low quality • advertised quality (qa) is controlled by seller Seller : Max payoff function π(x, qr, qa) = G (x, qr, qa) – c(x, qr) x ≡ volume of sale G() ≡ gross revenue c() ≡ cost

14. eBay Reputation System Feedback profile: R= (∑(+), ∑(-), ∑(no ratings)) Buyer Utility: U = θ *q – p p = price q = level of quality after consumption θ = buyer’s quality sensitivity Buyer estimated quality qe = f( qa, R) qa – advertised quality R - Reputation Buyer: max E(utility) = Ue = θ *qe – p After purchase: buyer observes q = qr + ε

15. eBay reputation system Error term (ε) represents: • buyers misinterpreting qa • sellers may vary in actual q from one transition to another • buyers may have small difference in q, based on outside factors like weather • some aspects of q depends on factors outside seller’s control (i.e. post office delays)

16. eBay reputation system Buyer satisfaction: S = U – Ue = θ (qr – qe + ε), ε ~ N(0, σ) Rating function r(S) : ‘+’ if S>0 ‘-’ if S <= - λ no rating if –λ <S<= 0 • Ratings as a function of a buyer’s satisfaction relative to expectations • λ accounts for e-bay buyers giving few ‘-’ ratings to sellers Possible Explanations: • Fear of reciprocal ratings • outside network communication between sellers and buyers • “culture of praise” : buyers feel a moral obligation to give “+” ratings

17. Conditions for a “well-functioning” reputation mechanism (RM) : • If there exists an equilibrium of prices and qualities under perfect information (qe=qa=qr), then in markets where qr is private to sellers, the existence of a RM makes it optimal for sellers to settle down to steady-state pair of real and advertised qualities (qr, qa) • Assuming (1) holds, under all steady-state seller strategies (qr, qa) the quality of sellers as estimated by buyers before transactions take place must be equal to the true quality (i.e. qe =qr) -in competitive markets: if qr > qe, then sellers would leave the market if qr < qe, then buyers would leave the market

18. Can they be well-functioning? • If given a rating function whether condition 2 is satisfied depends on the relationship between this rating function and the quality estimation function • Seller’s find it optimal to settle down to steady-state advertised quality levels if buyers are lenient when rating seller’s profiles

19. Estimated vs. Real Qualities in Steady State • The focus is on binary reputation mechanisms satisfying condition 2 • Denote an estimated quality function qe and the deception factor ξ • If ξ > 0, buyers will overestimate seller’s true quality • If ξ < 0, buyers will underestimate seller’s true quality • Let N be total no. of sale transactions [N= ∑(+) + ∑(-) + ∑(no ratings)] • Note: eBay does not specify quality assessment function f, it just publishes ∑(+) and ∑(-) allowing buyers (users) to use function they see fit. It also does not publish ∑(no ratings) thus N is not known.

20. Estimated vs. Real Qualities in Steady State Continued • We will explore whether binary reputation systems can be well functioning • Let ξ(R) be an estimate of seller’s deception factor based on information contained in the seller’s profile • A binary reputation system where buyers • Rate according to r(S) • Assess item quality according to (5) • Have reliable rule for calculating ξ(R) for a given seller satisfies condition 2 • Aside: We would not expect any profit maximizing seller to under-advertise

21. Estimated vs. Real Qualitiesin Steady State Continued • There are three ways buyers may use ∑(+), ∑(-), and N to estimate ξ(R) • Based on the number of positives • Based on the number of negatives • Based on the ratio between negatives and positives

22. Estimate based on positives • Require a fraction of positive ratings exceed a threshold, η^ • We will use statistical hypothesis, • test null hypothesis Ho: η ≥ 0.5 given η^ • We get new quality assessment function, qe • Method is appealing due to its relatively simplicity • Although, it is difficult without knowledge of N (Recall N is not specified by eBay) • Conclusion, method is rarely used by eBay users

23. Estimate based on Negatives • This method is similar to previous, except we are know looking at fraction of negative ratings, ζ • Again using statistical testing • Null hypothesis, Ho’: ζ ≤ k* , where k* is a monotonically decreasing function of the leniency factor λ • New quality assessment function, qe • Conclusion, satisfaction of condition 2 is always possible. In order to find k* we need parameters λ, θ, and σ. However, this are not available to buyer’s in practice and the right k* is very important to the well-functioning of the mechanism. But parameters can be derived from ∑(+), ∑(-), and N. • Overall, this function is a rather fragile rule for assessing the seller’s quality efficiently

24. Estimate based on Negatives Continued • Other things to consider: • What methods they use to compute threshold • Whether their trustworthiness thresholds do indeed come close to satisfying condition 2 • These open questions invite to further explore empirical and experimental results to complement this paper

25. Estimate based on ratio between negative and positives • We can just try to find a quality assessment function between positive and negative ratings, such a function will not exists • Let ρ(ξ) = ∑(-) / ∑(+), so this function is non-negative and monotonically increasing in ξ • Again using statistical testing • Null hypothesis, Ho”: ρ^ ≤ 2*Φ[-λ / (θσ)] where Φ() is the standard normal CDF • New quality assessment function qe • Once again we need knowledge of parametersλ, θ, and σ which is not known but can be substituted by N if buyers have knowledge of it. • Conclusion, this problem is just as difficult as estimation on negative ratings.

26. Existence of Steady-State • We want to show function based on number of negative ratings to find quality assessment function are preferred to the one’s using just the number of positive ratings • To show let’s observe what would occur if sellers oscillate between good and bad quality • Let’s say in period 0 seller had N transactions with a good reputation, q* • If in period 1, she milks reputation earned during period 0 (in order to make a little more profit since item being sold this period is not as in good conditions) • Seller’s subsequent estimate quality will fall to zero. But in order to re-gain their good reputation, seller will have to reduce the ratio ∑(-) / N and the threshold k* (this action will occur when seller’s places a good item at a lower price)

27. Existence of Steady-State Continued • Conclusions • A profit maximizing seller will oscillate if profit of ‘deceiving’ transaction exceeds the loss from ‘redeeming’ transaction both relative to steady-state profit • However, seller’s will require many more ‘redeeming’ transactions after a ‘deceiving’ one. Thus, if λ is sufficiently large sellers will find it optimal to settle down to steady-state real and advertised quality levels

28. Reality Checks • Assumptions: • All buyers have the same quality sensitivity, θ and leniency factor, λ • Buyers always submit ratings when satisfaction is above 0 or falls below –λ Not likely to hold in real market!

29. Reality Checks: • Some buyers never rate • Buyers differ in sensitivity and leniency • Relax both assumptions HOMEWORK Modify r(S) to account for some buyers never rating

30. Conclusion • Binary Reputation Systems can be well-functioning provided buyers find the right balance between leniency and quality assessment • Finding this balance when judging seller’s profiles is necessary for the well-function of the system, otherwise the resulting market outcome will be unfair

31. Low-Valued vs. High-Valued Items Pennies from eBay: the Determinants of Price in Online Auctions By: David Lucking-Reiley, Daniel Reeves and Doug Bryan/Naghi Prasad (2000 draft) Valuing Information: Evidence from Guitar Auctions on eBay By: David H. Eaton (2002)

32. U.S. Cents • Collected data over 30-day period, July-Aug 1999 • 20,292 observations (referred to as the large set) • Subset of these used, on auctions of “U.S. Indian Head Pennies” • 461 such auctions (referred to as the small set)

33. Experiments Conducted • Experiments and regression analysis on three types of parameters: • Effect of positive and negative feedback • Effect of auction length • Effect of minimum bid and reservation prices

34. Results • Result 1- • A 1% increase in positive feedback → 0.03% increase in auction price • Effect of 1% negative feedback → 0.11% decrease in auction price (this statistically significant at 5%) • Result 2- • Also found length of auction positively influenced price, longer auctions higher prices • 3 & 5-day auctions almost had same prices, but 7-day auctions increased by 24% while 10-day auctions increased by 42% (both statistically significant) • Result 3- • The presence of reserve prices increased price by 15% • as minimum price bid increases by 1% final price increases by less than 0.01%

35. Low-Valued vs. High-Valued Items Pennies from eBay: the Determinants of Price in Online Auctions By: David Lucking-Reiley, Daniel Reeves and Doug Bryan/Naghi Prasad (2000 draft) Valuing Information: Evidence from Guitar Auctions on eBay By: David H. Eaton (2002)

36. Paul Reed Smith Guitar Auctions • High valued item (price > $1000) • Some knowledge of item based on reputation of original product ( i.e. manufacturer reputation) • Information signals: • feedback profile • availability of escrow services/ fraud protection • pictures

37. PRS Guitar Auctions Data: • auctions between January – April 2001 • four model classes • 325 successful auctions

38. PRS Guitar Auctions Empirical Results: • pictures attract more bidding action and increase final bid price (added value $60-232 / bid) • Use of escrow services send a negative signal to buyers • Negative feedback: - decreases the likelihood of sale - increases the final bid price for item (added value ~ $504)

39. Last-minute bidding Last-Minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet By Alvin E. Roth and Axel Ockenfels

40. Late bidding Rules for ending auction: • E-bay: fixed end-time • Amazon: automatic 10 minute extension on end time whenever bidding continues

41. Late bidding Observations: the effect of experience in late bidding • More late bidding on e-bay than on Amazon • e-bay: experienced bidders submit late bids more often than less experienced bidders (opposite for Amazon) • e-bay: more late bidding for antiques than for computers

42. Last-minute bidding (“sniping”) • E-bay advices buyers to bid early (i.e. proxy bidding) • Late bids: risk of not being successfully transmitted • lower expected revenues for sellers • Esnipe.com “sniping” is a best response to e-Bay fixed deadline!

43. Last-minute bidding • Theorem 1: A bidder in continuous-time second-price private value auction doesn’t have any dominant strategies

44. Notation: Notation m = min initial bid s – smallest increment possible Vj – willingness to pay for bidder j ~ F Consider two bidders : i, j Show: bidder j with value Vj > m+s has no dominant strategy to every strategy of bidder i

45. Proof (cont’) Case 1: player i strategy: bid m at t=0, not bid if she remains the highest bidder bid B (with B> Vj+s) whenever she is not the highest bidder player j best response: Not bid at any time t<1 Bid Vj at t=1 (end of auction) Payoff to player j = p*(Vj – m- s)>0, p=probability bid is transmitted Case 2: Player i strategy: not bid at any time If player j uses her previous strategy: E[payoff]= p*(Vj – m) < Vj –m Player j has no dominant strategies!

46. Last-minute bidding • Recall Theorem 1: A bidder in continuous-time second-price private value auction doesn’t have any dominant strategies

47. Last-minute bidding • Theorem 2: There can exist equilibria in which bidders do not bid their true values until last moment (t=1), at which time there is only a probability p (p<1) that a bid will be transmitted

48. Proof: • A mutual delay until the last-minute of the auction can raise the E [profit] of all bidders because of the positive probability that another bidder’s last-minute bid will not be successfully transmitted • At this equilibrium, E [bidder profits]> than at equilibrium at which each player bids his true values early

49. Strategic Reasons for Late Bidding • To avoid “bidding wars” with incremental bidders • To avoid “bidding wars” with other like-minded bidders • To protect information

50. Non-strategic Reasons for Late Bidding • Procrastination • To retain flexibility to bid in other auctions (same item)