Si Sign gnalin aling g Sc Sche heme mes fo for Re Reve - - PowerPoint PPT Presentation

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Mar 26, 2023 614 likes •1.15k views

Si Sign gnalin aling g Sc Sche heme mes fo for Re Reve venu nue Max e Maxim imiz izati ation on Yuval Emek Michal Feldman Iftah Gamzu (ETH Zurich) (HUJI and Harvard) (MSR) Moshe Tennenholtz Renato Paes Leme (MSR and

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Si Sign gnalin aling g Sc Sche heme mes fo for Re Reve venu nue Max e Maxim imiz izati ation

Yuval Emek (ETH Zurich) Michal Feldman (HUJI and Harvard) Iftah Gamzu (MSR) Renato Paes Leme (Cornell) Moshe Tennenholtz (MSR and Technion)

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Which infor

matio tion to re reve veal in the interface of AdExchange and how does that affect re reve venue and wel elfar are ?

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web surfers =

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web surfers =

p1 p2 p3 p4 p5

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ad slot

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ad slot

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ad slot AdExchange

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ad slot AdExchange holds a second price auction

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ad slot AdExchange holds a second price auction

Music Store re Pop p Art Supp ppli lies

b1 b2 b3

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ad slot AdExchange holds a second price auction

Music Store re Pop p Art Supp ppli lies

Their value depends who is the user behind the impression.

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web surfers =

p1 p2 p3 p4 p5 0.1 15 10 20 5

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web surfers =

p1 p2 p3 p4 p5

Pop p Art Supp ppli lies

0.1 15 10 20 25 10 0.1 0.1 0.1 5

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web surfers =

p1 p2 p3 p4 p5

Pop p Art Supp ppli lies

0.1 15 10 20 25 10 0.1 0.1 0.1 5

Music Store re 10

20 1 5 0.2

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web surfers =

p1 p2 p3 p4 p5

Pop p Art Supp ppli lies Music Store re

…… …… …… ……

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Who knows what ?

AdExchange knows who is the user j

issuing the click

Advertisers just know the prior p

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One idea: revealing all the information

Advertiser i bids
Revenue =

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One idea: revealing all the information

Advertiser i bids
Revenue =
Many problems:
Cherry picking
Revenue collapse
Adverse selection
Too much cognitive burden

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web surfers =

p1 p2 p3 p4 p5

Pop p Art Supp ppli lies

0.1 15 15 15 25 0.1 0.1 0.1 0.1 0.1

Music Store re 0.1

25 1 5 0.2

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web surfers =

p3 p4 p5

Pop p Art Supp ppli lies

15 15 15 0.1 0.1 0.1

Music Store re

1 5 0.2 p1 + p2 13 0.1 13

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web surfers =

p1 + p2 p3 + p4 + p5

Pop p Art Supp ppli lies

15 13 0.1 0.1

Music Store re

13 1

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Other idea: bundling the items

Group the items in sets S1 … Sn
Revenue =

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Other idea: bundling the items

Group the items in sets S1 … Sn
Revenue =
[Ghosh, Nazerzadeh, Sundarajan ‘07]

[Emek, Feldman, Gamzu, Tennenholtz ‘11]

strongly NP-hard to optimize revenue
2-approximation

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Other idea: bundling the items

Group the items in sets S1 … Sn
Revenue =
[Ghosh, Nazerzadeh, Sundarajan ‘07]

[Emek, Feldman, Gamzu, Tennenholtz ‘11]

strongly NP-hard to optimize revenue
2-approximation

Integral Partitioning Problem

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Bundling the items fractionally

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Bundling the items fractionally Signaling

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Bundling the items fractionally Signaling

[Emek, Feldman, Gamzu, Paes Leme, Tennenholtz ’12]
[Bro Miltersen, Sheffet ‘12]

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Signaling

Design a signal which is a random variable

correlated with j

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Signaling

Design a signal which is a random variable

correlated with j

and is represented by a joint

probability

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Signaling

Design a signal which is a random variable

correlated with j

and is represented by a joint

probability

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Signaling

For user j, the search engine samples

according to

Advertiser use to update their bid

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p1 p2 p3 p4 p5

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j=3

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j=3

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j=3

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j=3 p’1 | p’2 | p’3 | p’4 | p’5 |

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Signaling

Expected revenue:

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Signaling

Expected revenue:

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Signaling

Expected revenue:
How big does s (size of signaling space) need to be ?
How to optimize revenue ? (ma

max2 is not convex)

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Signaling

Theorem: If there are n advertisers, we just need

to keep n ( (n-1) 1) signals. One correspond to each pair of advertisers (i1, i2)

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Signaling

Theorem: If there are n advertisers, we just need

to keep n ( (n-1) 1) signals. One correspond to each pair of advertisers (i1, i2)

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Signaling

Theorem: The revenue-optimal signaling can be

found in polynomial time.

Also, there is an optimal signaling scheme that

preserves ½ of the optimal social welfare.

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Signaling

Theorem: The revenue-optimal signaling can be

found in polynomial time.

Also, there is an optimal signaling scheme that

preserves ½ of the optimal social welfare.

It improves the optimal (integral) bundling up to

a factor of 2.

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Signaling in a Bayesian World

Valuations of advertiser i for user j depends on

some unknown state of the world

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Signaling in a Bayesian World

Valuations of advertiser i for user j depends on

some unknown state of the world

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Signaling in a Bayesian World

Valuations of advertiser i for user j depends on

some unknown state of the world

Let
We can find the optimal signaling scheme in

polynomial time if

Naïve extension of the full information LP

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Signaling in a Bayesian World

If m (number of user types) is constant, then we

can find the optimal signaling scheme in time polynomial in k,n.

Geometry of hyperplane arrangements

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Signaling in a Bayesian World

If m (number of user types) is constant, then we

can find the optimal signaling scheme in time polynomial in k,n.

Geometry of hyperplane arrangements
NP-hard: n=3 and arbitrary m,k

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Signaling in a Bayesian World

If m (number of user types) is constant, then we

can find the optimal signaling scheme in time polynomial in k,n.

Geometry of hyperplane arrangements
NP-hard: n=3 and arbitrary m,k
Open: approximability of this problem

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Approximability in the Bayesian Case

Open Problems

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Approximability in the Bayesian Case Bayesian case with independent values

Open Problems

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Approximability in the Bayesian Case Bayesian case with independent values Optimal auctions with signaling

Open Problems

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