week 5 1

COS 444 Internet Auctions:

Theory and Practice

Spring 2010

Ken Steiglitz ken@cs.princeton.edu

week 5 2

week 5 3

Field Experiment“ Public Versus Secret Reserve Prices in eBay Auctions:

Results from a Pokémon Field Experiment,” R. Katkar & D. Lucking-Reiley, 1 December 5, 2000.

“We find that secret reserve prices make us worse off as sellers, by reducing the probability of the auction resulting in a sale, deterring serious bidders from entering the auction, and lowering the expected transaction price of the auction. We also present evidence that some sellers choose to use secret reserve prices for reasons other than increasing their expected auction prices.”

week 5 4

Pros and cons of secret reserve

Pros:• By comparison with equal open reserve, attracts

bidding activity, which is generally good because 1) more bidding attracts more bidders, 2) bidders fear “winner’s curse” less with more revealed information (more later, Milgrom & Weber 82),

and so bid higherCons:• Sends signal that price will be high, discourages

entry• Extra fee on eBay

week 5 5

Field Experiment… Katkar & L-R 00

• 50 matched pairs of Pokémon cards• 30% book value, open & secret reserve• Open reserve increased prob. sale: 72% vs.

52%• Open reserve yielded 8.5% more revenue• Caution: these are low-priced items!• Caution: is it reasonable to match equal secret

and open reserves? Is this the right question? Use low opening? Risk on high-value items ?

• Evidence of illicit transactions around eBay

week 5 6

Field Experiment… Katkar & L-R 00

Notice that they “… concluded with a notice that we intended to use data on bids for academic research, and provided contact information for questions or concerns.”

• Do you think this affected results?

week 5 7

All-Pay auction

• Here’s a different kind of auction: High bidder wins the item All bidders pay their bids! … the All-Pay Auction

• Models political campaigning, lobbying, bribery, evolution of offensive weapons like antlers,… etc.

• What’s your intuiton? How do you bid? Is this better or worse for the seller than first-price? Second-price?

week 5 8

All-pay equilibrium

Start with your value = v

E[surplus] = pr{1 wins} [ v ] – b ( v )

pay in any event

In value space, “bid as if your value = z”

E[surplus] = vF(z)n-1 – b(z)

And set derivative to zero at z=v.

week 5 9

All-pay equilbrium, con’t

• Differentiating and setting z=v:

0)()()()1( 2 vbvfvFvn n

• Integrating and using b(0)=0:

v nydFyvb0

1)()(

• Uniform-v case:

n

nv nv n vdyyyydvb n1

10

1

0

1 )1()()(

Note: once again, b΄ > 0, verifying monotonicity.

week 5 10

Expected rev. for uniform v’s of all-pay = FP = SP

• In all-pay auction, E[pay] = bid• Averaging over v for each bidder:

• Times n bidders:

• Same as SP, FP! More revenue equiv.!

1

1111

0 n

n

ndvnv

n

n

1

1E[revenue]

n

n

week 5 11

Related to all-pay: War of Attrition

Suppose two animals are willing to fight for a time (b1, b2). One gives up, the other wins. The price paid by the winner is

min (b1, b2).

Essentially a second-price all-pay: the winner pays second-highest bid, losers pay their bids.

week 5 12

Rev. equiv. FP=SP for general distributions

• In SP auctions, expected revenue = expected price paid = expected value of second-highest bid in equil.

1

0 2

1

0 22 )(1)(][ dxxGxdGxYERsp

In equil. means truthful bidding in SP auctions, of course.

week 5 13

Rev. equiv. FP=SP for general distributions

• In FP auctions, expected revenue = n E [payment of bidder 1 in equil.] = n E [bfp(v1 ) pr{1 wins} ]

1

0

1 )()()( vdFvFvbnR nfpfp

1

0

1

)(

)()(

n

v n

fp vF

ydFyvb

Now just plug in the known equil. bidding function:

week 5 14

Rev. equiv. FP=SP for general distributions

… and use integration by parts mercilessly, yielding

1

0

1

0

1 )1(1 dvFndvFn nn

spRdvG 1

0 21

1

0 0

1 )()(v n

fp vdFydFynR

week 5 15

Notice that this is also the revenue for general distributions in the all-pay auction

1

0 0

1 )()(v n

fp vdFydFynR

1

0)()( vdFvbn ap

week 5 16

Back to eBay: timing of bids

Pro sniping (strategic):• Avoids bidding wars• Avoids revealing expert information

(if you are an expert) [Roth & Ockenfels 02, Wilcox 00]

• Avoids being shadowed (possible?)• Possibly conceals your interest entirely• [Ockenfels & Roth 06] suggest implicit

collusion (a weak version of the prisoner’s dilemma)

week 5 17

[Roth & Ockenfels 02, Wilcox 00] Evidence from the field

Roth & Ockenfels: Computers vs. antiques

Wilcox: Power drills, etc. vs. pottery

• Bidding on collectibles later than bidding on

commodities• eBay bidding later than on Amazon (where deadline

is extensible)• Bidders with high feedback later than those with low

feedback on eBay

week 5 18

[Ockenfels & Roth 06] Argument pro sniping

• Suppose there is a significant chance of a snipe missing the deadline

• Then sniping can amount to “implicit collusion”, similar to an iterated prisoner’s dilemma

Depends on assumption of unreliable sniping (?, see eSnipe, eg)

week 5 19

[Ockenfels & Roth 06] Argument pro sniping

• Suppose two bidders, each misses deadline with prob. ½

• Each decides to bid truthfully

• Each decides to bid exactly once, either early or late (snipe)

• Each has private value = $21

• Starting bid = $1

week 5 20

[Ockenfels & Roth 06] Argument pro sniping

Game matrix, expected payoffs

5/510/0

0/100/0

late

early

lateearly

Defect

Cooperate

week 5 21

[Ockenfels & Roth 06] Argument pro sniping

Game matrix, expected payoffs

5/510/0

0/100/0

late

early

lateearly

An iterated Prisoner’s Dilemma!Actually, “Friend or Foe” game show because 0/0 is a weak equilibrium

See Axelrod, EvolutionOf Cooperation, BasicBooks, NY, 1984

week 5 22

Back to eBay: timing of bids

Pro sniping (nonstrategic):• Delays commitment• Or just procrastination• Soon-to-expire may be displayed first in

search• Willingness to pay increases with time --- “endowment effect” [Knetsch & Sniden

84, Kahneman, Knetsch, Thaler 90, Thaler 94]

week 5 23

Back to eBay: timing of bids

Anti sniping (strategic early bidding):

• Scares away competition

• Raising one’s own bid even scarier

• [Rasmusen 06] suggests cost of discovery leads to a collusive equilibrium

week 5 24

[Rasmusen 06]Argument pro early bidding

• Bidder 1 is uncertain of her value, can pay cost c to discover; bidder 2 is certain of his value

• 1 starts with low bid• 2 bids early to signal if his value is high• 1 pays to discover her value on signal• With carefully chosen c this is mutually beneficial --- an asymmetric equilibrium

Do you believe this?

week 5 25

Back to eBay: timing of bids

Anti sniping (nonstrategic early bidding):

• Allows you to sleep, eat, etc. (But sniping services and software solve this problem.)

• Psychological reward for being listed as high bidder

• Sniping may be perceived as underhanded, cowardly, unethical