Online Ad Slotting with Cancellations

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Online Ad Slotting with Cancellations
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Advance-booking of ad slots

• Not available in current ad systems
• Advertisers can only bid in spot auction
• Desired by publishers and advertisers
• Reduces uncertainty
• Widespread use for traditional ads
• Goal competitive worst-case mechanism
• Automation across varying sites
• No need to rely on estimates

3
1
Your ad here
November 5, 2008
Need to know now
10
Seller Yes/No
Your ad here
Ur ad hr
Book today future slots!
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Online decision problem
Online weighted bipartite matching
Your ad here
2
2PM, 2
Your ad here
2
3
4PM, 3
3
Ur ad hr

• Bids for slots arrive sequentially
• Decision must be taken online
• Goal efficient allocation (matching)

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Online weighted bipartite matching
Your ad here
November 5, 2008
1
10
Ur ad hr
Your ad here
No worst-case guarantee possible if arbitrary
values/arrivals
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Online weighted bipartite matching

• No worst-case guarantees if arb. values/arrivals
• We assume
• the seller can cancel reservations
• at a cost to the bidders
• Assumptions in literature
• Bids arbitrary arrive in uniformly random order
• Bounded values
• Costly cancellations (same as us) next talk

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Online weighted bipartite matchingwith selfish
players
Ur ad hr
Your ad here
2K
7K
2K
1K
3K
3K
Your ad here

• You canceled MY reservation?!
• How can I make money off you?

Additional goal robust to
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This talk advance-booking with cancellations
for selfish players

• Favorable game theoretic properties
• Efficiency constantoptimal
• Revenue constantVCG

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Bidder model
at arrival time
A
Ur ad hr
B
Your ad here
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bidi
Your ad here
C

• Bidder wants one slot out of a subset (B or C)
• Same private value for any slot
• Seller knows is desired slots

0, if not promised valuei, if
allocated ??valuei, if bumped
One bid per bidder. Immediate yes/no required.
utility
net payment
? lt1
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Advance-booking mechanism
extends offline approximation algorithm for
weighted bipartite matchingMcGregor2005
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Ai
Si
0
8
bumped
survive
bidi
not accepted
accepted, paid
accepted, pays
bids
Ur ad hr
9
1
0
8
0
X
5
5
6
0
2
0
to be paid
Your ad here
3
10
10
12
4
18
18
needs 18 to be accepted
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Ai never changes, but Si does Both depend on
other bids
Survivors will pay seller
Accept if can reshuffle bid (11)bumped bid
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Ai
Si
0
8
bumped
survive
bidi
not accepted
accepted, paid
accepted, pays
Pays to seller
Paid by seller ?bidiltbidi
No money transfer
Compensations and payments
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Ai
Si
0
8
bumped
survive
bidi
not accepted
accepted, paid
accepted, pays
0
bids
pays 8 - ?8
Ur ad hr
9
1
0
X
5
6
0
2
paid 5?
Your ad here
3
10
10
pays 10
12
4
18
18
16
Accept if can reshuffle bid (11)bumped bid
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Should bid at least true value
Best bid
Best bidtrue value
Best bidS-e
S
(survive)
(get best refund)
True value
Your ad here
Your ad here
S
A
0
paid ?bid
?
pays
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Ai
Si
0
8
bumped
survive
bidi
not accepted
accepted, paid
accepted, pays
bids
Ur ad hr
Refunded fraction
Improv factor
X
5
paid 5?
Your ad here
Need
Accept if can reshuffle bid (1?)bumped bid
Accept if can reshuffle bid (11)bumped bid
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Efficiency

• McG survivors (1?) approx to OPT on bids
• Survivors constant approx to OPT on values
• If sum of utilities is positive
• Guarantee even with somewhat rational players

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Effective efficiency

• Defn Survivors bids ? bumped bids
• Sum of all bidders effective values
• Our algo constant approx to OPT on values
• If sum of utilities is positive
• Competitive ratio
• In 0,1 high good algorithm
• Standard worst-case performance measure

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Ai
Si
0
8
bumped
survive
bidi
not accepted
accepted, paid
accepted, pays
Pays to seller
Paid by seller ?bidiltbidi
No money transfer
Why good revenue
Compensations and payments
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Revenue

• Payments refunds VCGbids/constant
• Bids values
• Bidding value is better than ltvalue regardless
• Payments refunds VCGvalues/constant

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Speculators
FREE MONEY!
If can guess others bids
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Speculators

• Speculators not interested in ads, just money
• value 0 can arrive at any point in time
• Bound on their profit
• Can locally hurt revenue
• If speculators do not run a loss
• Efficiency Ct approx to optimal
• Can locally hurt efficiency
• Instances with no pure Nash equilibrium

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What if refund ?S, not ?bid?

• more truthful bid-independent
• But seller might lose money

1PM, 1
S11000/(1?), paid by seller
Your ad here
2PM, 1000
S21?, paid to seller
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Impossibility MyersonSatterthwaite

• Thm No offline algorithm for trading can
• Optimal assignment
• No money needed to run the algorithm
• Truthfulness
• No honest bidder runs a loss
• Our setting online do not know the future
• Approximately optimal
• Revenue a constant factor away from VCG
• Bid true value survivors should be truthful
• No honest bidder runs a loss

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What if desired slots not known?
Utility from refund
Utility 1 from alloc
Ur ad hr
Ur ad hr
1PM, 1
1PM,
Your ad here
Your ad here
2PM, 1000
2PM, 1000
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Conclusions advance booking with cancellations
for selfish players

• Useful to be flexible, i.e. revise decisions
• Bidders should bid at least true value
• Survivors best response is to be honest
• Value of assignment
• 1? approximation wrt bids
• If bidders bid well, constant approx wrt values
• Revenue constant approximation to VCG

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Extensions

• Insurance pay more for higher ?, ?
• Improvement of results if prior

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You survived!
Please pay me with questions
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Commit/not commit

• When bidding, a bidder makes private choice
• Commit will incur an ?v cost if bumped
• Not commit 0 value if winner

• Pricing scheme ensures for honest commit
  survivor
• (Commit, survive) gt (not commit, bumped)

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Matroids

• Abstract combinatorial structures
• Generalize matchings, spanning trees etc
• Independent subsets of set G
• If X?G indep, any subset of X also indep
• If X, Y indep, XgtY, then ? x in X\Y such that
  Y?x is also indep (exchange)

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Bidders indep if can be matched

• If X, Y indep, XgtY, then ? x in X\Y such that
  Y?x is also indep (exchange)

x
x
Ur ad hr
Ur ad hr
Ur ad hr
i
Your ad here
Your ad here
Your ad here
X
Y
y
Y?x
y
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Algorithm, more formally
?M
j

• M ??
• For each bidder i
• If ?? augm path P ending in
• unmatched item or
• bidder j with bi(1?)bj
• Then M M ? P

Ur ad hr
?M
?M
Your ad here
?M
i
augmenting path P
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Algorithm, more formally
?M
j

• M ??
• For each bidder i
• If ?? augm path P ending in
• unmatched item or
• bidder j with bi(1?)bj
• Then M M ? P

Ur ad hr
?M
?M
Your ad here
?M
i
O(bidders slots)
augmenting path P
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If bid truthful, survivor does not regret it
S
Your ad here
Your ad here
A
0
8
paid ?bid
?
pays
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If bid truthful, survivor does not regret it
S
Your ad here
Your ad here
A
8
true value
0
paid ?bid
?
pays
If AltS, max refund is ?S, i.e. discount if win
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If bid truthful, survivor does not regret it
Your ad here
AS
true value
0
8
?
pays S

• If AS, fixed price of S