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Problem set 2 Market Design...

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Question 1 (a) Explain (briefly) why some bidders perceive eBay auctions as an English outcry auction. The auction format followed by eBay is a second price auction incorporating features of an English outcry auction and second-price auction. This means that eBay auction follow the bidding rules of English outcry auction, but it charges the winner by the sum of the second highest bid and the bid increment. However, there is the case that some bidders perceive eBay auctions as an English outcry auction. This is because there is a situation that a bidder bids the minimal amount, but his/her bid is the highest bid amount at that time. Therefore, the sum of the second highest bid and the bid increment will be higher than his/her bid. As this happens, the winner will have to pay eBay by the amount of bid that he/she made instead because eBay will never charge a bidder more than his/her valuation. (b) Provide at least two take-aways from Roth and Ockenfels’ analysis of eBay and Amazon auctions. - The paper by Roth and Ockenfel compares between eBay and Amazon auctions. They say that these two auctions follow almost the same rule which both auctions follow the format of English ascending auction, proxy bidding and second-price auction. Nonetheless, while eBay has a hard deadline and allows bid snipping (last minute bidding), Amazon has used a soft rule to set the deadline in order to prevent bid snipping. In other words, the auction on eBay will end exactly at the time that sellers set. Nevertheless, whenever there is a bid snipping on Amazon auction (somebody bid in the last minute of the auction), the auction deadline will be extended for other bidders to respond. - It is important to note that late bidding is rational with interdependent/common values. The allowance of bid snipping could have both advantage and disadvantage. On the good side, a bid snipping will eventually prevent the seller from using shill bidders to bid against the real bidders. Moreover, a bidder could win the auction at the incremental bidder’s low initial bid by bidding late. On the other hand, when the snipping is not successfully transmitted, sellers might get the lower revenue as it prevents more late bidders who have a higher valuation to bid and those late bidders will not get the item that they want. - After Roth and Ockenfel gathered the data from eBay and Amazon in both computer (private values) and antique (interdependent values) categories, they found that there are more snipping on eBay than Amazon for both categories. The authors further point out that experienced bidders bid significantly later on eBay. Therefore, they conclude that auction design can influence bidders’ behaviour of bidding and hard deadline give incentive for bidders to bid late. Additionally, there is a strong effect with bid snipping whenever experienced bidders participate in the auction and bidders have interdependent values. Question 2 Consider an environment where 2 items (X and Y) are for sale, and there are three bidders (A, B, and C) who each want at most one license. The values of the bidders are

X

Y

A

40

35

B

60

50

C

80

60

Calculate the outcome of the VCG auction

A

B

C

X

40

60

80

Y

35

50

60

A

B

C

Social value

Assignment 1 X

Y

0

40+50 = 90

Assignment 2 Y

X

0

35+60 = 95

Assignment 3 0

X

Y

60+60 = 120

Assignment 4 0

Y

X

50+80 = 130

Assignment 5 X

0

Y

40+60 = 100

Assignment 6 Y

0

X

35+80 = 115

The assignment that maximize the social value is then assignment 3, so we have:

*(A) = 0, *(B) = Y, *(C) = X - There are 3 bidders and each bidder only want one item. - In this case, it is noticed that, for either X or Y, bidder C is a bidder with the highest valuation, bidder B is a bidder with the second highest valuation and bidder A is a bidder with the lowest valuation. So, the assignment of the item will not be affected by the present or absent of bidder A. - If bidder C is present: assignment that maximizes social value is C gets X, B gets Y and A gets nothing. - If bidder C is absent: assignment that maximizes social value is C does not get the item, A gets Y and B gets X. - If bidder B is present: assignment that maximizes social value is B gets Y, C gets X and A gets nothing. - If bidder B is absent: assignment that maximizes social value is B does not get the item, A gets Y and C gets X. - Price for bidder A is 0. - Price for bidder C is (35 + 60) – (50) = 45 - Price for bidder B is (35 + 80) – (80) = 35 - Therefore, bidder C pays 45 for item X and bidder B pays 35 for item Y. Question 3 We consider a keyword auction for search engines for two links. The first link has a click frequency of 200/week and the second link has a click frequency of 100/week. Three bidders compete for that keyword. Bidder A values the pay-per-click at 8, bidder B’s valuation is 5 and bidder C’s valuation is 10. The auction format is GSP and we assume bidders bid their valuations. Calculate the outcome. Auction format: GSP Let link 1= 200clicks/week and link 2= 100clicks/week vC = $10/click > vA = $8/click > vB = $5/click.Due to the bidders bid their own valuations - Link 1 spot awarded to bidder C, and C has to pays $8/click. - Link 2 spot awarded to bidder A, and A has to pays $5/click. - Bidder B does not get assign to any link because B has the lowest valuation. So, bidder B does not has to pay and B’s payoff is 0.

- Payoff of bidder C: ($10 – $8) * 200 = $400. - Payoff of bidder A: ($8 – $5) * 100 = $300. - Bidder C has to pay: 8*200 = $1600/week. - Bidder A has to pay: 5*100 = $500/week. Question 4 We consider a GSP auction with four bidders, A, B, C and D. Since there are four bidders only the three highest bidders will be displayed). The click frequency of the first, second and third positions are 100 clicks/hour, 75 clicks/hour and 35 clicks/hour, respectively. Bidders’ valuation per click are vA = 10, vB = 6, vC = 4, vD = 3. Bidder B, C and D bid 5, 3 and 1, respectively. What is the optimal bid for A? 1 = 100clicks/hour, 2 = 75clicks/hour, 3 = 35clicks/hour vA = $10/click, vB = $6/click, vC = $4/click, vD = $3/click bB = 5 > bC = 3 > bD = 1

Position

Bidder A’s bid

Bidder A’s payoff

1

bB = 5 < b A

(10 – 5) * 100 = $500

2

bC = 3 < b A < b B = 5

(10 – 3) * 75 = $525

3

bA < bC = 3

(10 – 1) * 35 = $315

From the table above, we can conclude that bidder A will get the highest payoff when he/she is assigned to the second position. Hence, the optimal bid that will maximize the payoff for bidder A must be any bid amount that is higher than $3 and lower than $5....