fo for Sel r Selli ling ng In Info form rmation ation Moshe - - PowerPoint PPT Presentation

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fo for sel r selli ling ng in info form rmation ation
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fo for Sel r Selli ling ng In Info form rmation ation Moshe - - PowerPoint PPT Presentation

May 21, 2023 8 likes •621 views

Op Opti tima mal Mec l Mecha hani nism sms fo for Sel r Selli ling ng In Info form rmation ation Moshe Babaioff Robert Kleinberg Renato Paes Leme (MSR-SVC) (Cornell) (Cornell) The Secret Agent The Secret Agent Moscow London

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Op Opti tima mal Mec l Mecha hani nism sms fo for Sel r Selli ling ng In Info form rmation ation

Moshe Babaioff (MSR-SVC) Robert Kleinberg (Cornell) Renato Paes Leme (Cornell)

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SLIDE 2

The Secret Agent

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The Secret Agent Moscow London Valencia

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SLIDE 4

The Secret Agent The Informant Moscow London Valencia

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The Secret Agent The Informant The Information Moscow London Valencia

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The Secret Agent The Informant The Information Moscow London Valencia How to sell information ?

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SLIDE 7

Th This s is no s not (only) ly) a a tal alk ab about ut esp spiona

  • nage.

ge.

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SLIDE 8

The Advertiser The Data Provider The Information Potential ads to show How to sell information ? cookies, user data…

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The Secret Agent The Informant The Information Moscow London Valencia How to sell information ?

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The Secret Agent The Informant The Information Moscow London Valencia

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The Secret Agent The Informant The Information Moscow London Valencia

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SLIDE 12

The Secret Agent The Informant The Information Moscow London Valencia

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The Secret Agent The Informant The Information Moscow London Valencia Common Bayesian Prior

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The Buyer The Seller er The Information Moscow London Valencia Common Bayesian Prior

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More formally …

  • Seller knows .. Buyer knows .
  • Pair comes from a joint distribution

that is common knowledge

  • Buyer needs to pick an action

getting reward Co Context: text:

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SLIDE 16

Buyer (Secret Agent) Utility

  • If he doesn’t know (i.e. only knows )
  • If he also knows
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Buyer (Secret Agent) Utility

  • If he doesn’t know (i.e. only knows )
  • If he also knows
  • Expected surplus for full information
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Ho How mu w much h of th f this s su surp rplu lus can an the e se sell ller er (info formant) rmant) extract given that he doesn’t know w ? ?

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SLIDE 19

Why not post a price ?

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Why not post a price ?

  • with ¼ probability each
  • with ½ probability (danger level)
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SLIDE 21

Why not post a price ?

  • with ¼ probability each
  • with ½ probability (danger level)
  • if and 0 o.w.
  • if and 0 o.w.
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SLIDE 22

Why not post a price ?

  • with ¼ probability each
  • with ½ probability (danger level)
  • if and 0 o.w.
  • if and 0 o.w.
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SLIDE 23

Why not post a price ?

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Why not post a price ?

  • Post price 50 for the whole information

will generate revenue ½ ∙ 50 = 25

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Why not post a price ?

  • Post price 50 for the whole information

will generate revenue ½ ∙ 50 = 25

  • Post price 50 for and 0.5 for

will generate revenue ½ ∙ 50 + ½ ∙ 0.5 = 25.25

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SLIDE 26

Why not post a price ?

  • Post price 50 for the whole information

will generate revenue ½ ∙ 50 = 25

  • Post price 50 for and 0.5 for

will generate revenue ½ ∙ 50 + ½ ∙ 0.5 = 25.25 Infor

  • rmat

mation ion is a lot t mo more e flex exibl ible e than traditional goods.

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SLIDE 27

What is a feasible mechanism ?

message $$$ message $$$ message message message

Informant proposes a mechanism based on . and commits to faithfully follow it. The agent is strategic. Informant wants to maximize revenue.

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SLIDE 28

How to design optimal mechanisms ?

  • 1. Start with any possible interactive mechanism
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How to design optimal mechanisms ?

  • 1. Start with any possible interactive mechanism
  • 2. Show that they need to assume a particular format

(revelation principle still holds but is not enough)

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SLIDE 30

How to design optimal mechanisms ?

  • 1. Start with any possible interactive mechanism
  • 2. Show that they need to assume a particular format

(revelation principle still holds but is not enough)

  • 3. Optimize over the set of reduced mechanisms

(usually an infinite dimensional optimization problem)

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SLIDE 31

How to design optimal mechanisms ?

  • 1. Start with any possible interactive mechanism
  • 2. Show that they need to assume a particular format

(revelation principle still holds but is not enough)

  • 3. Optimize over the set of reduced mechanisms

(usually an infinite dimensional optimization problem)

  • 4. Give a structural characterization that brings it down

to a manageable (polynomial) size.

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SLIDE 32

How to design optimal mechanisms ?

  • 1. Start with any possible interactive mechanism
  • 2. Show that they need to assume a particular format

(revelation principle still holds but is not enough)

  • 3. Optimize over the set of reduced mechanisms

(usually an infinite dimensional optimization problem)

  • 4. Give a structural characterization that brings it down

to a manageable (polynomial) size.

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SLIDE 33

Independent and .

Theorem: If and are independent, there exists an

  • ptimal mechanism that offers to the buyer a list

where is a random variable correlated with and is its price.

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Independent and .

Theorem: If and are independent, there exists an

  • ptimal mechanism that offers to the buyer a list

where is a random variable correlated with and is its price. Examples: Yi is a “noisy” version of :

  • a subset of the bits
  • the XOR of two bits
  • with prob ½ and random with prob ½
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Independent and .

What does this theorem mean?

message $$$ message $$$ message message message

$$ $$

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Correlated and .

Theorem: If and are correlated, there exists an

  • ptimal mechanism that offers to the buyer a list

where is a random variable correlated with and is its price depending on the outcome of .

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Correlated and .

Theorem: If and are correlated, there exists an

  • ptimal mechanism that offers to the buyer a list

where is a random variable correlated with and is its price depending on the outcome of . We can find the optimal mechanism in polynomial time using convex programming.

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SLIDE 38

$$ $$ $$ $$

Independent case Correlated case

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What bad can happen ?

$$ $$

Correlated case

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What bad can happen ?

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What bad can happen ?

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What bad can happen ?

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What bad can happen ?

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What bad can happen ?

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What bad can happen ?

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What bad can happen ?

???

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What bad can happen ?

???

This mechanism doesn’t work if the buyer is allowed to defect at any point.

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One possible fix : large deposit upfront

$$ $$

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One possible fix : large deposit upfront

$$ $$

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One possible fix : large deposit upfront

$$ $$

Increases participation cost, creates incentives for the informant to defect, …

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Qu Questi estion

  • n:

Wh What at is t s the he re revenue enue op

  • ptimal

mal me mechanism anism wh wher ere (1) bu buye yer is all r is allow

  • wed

ed to

  • de

defe fect (2) no

  • po

posi siti tive ve tra ransfer sfers s ar are all e allow

  • wed

ed

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Th The an e answ swer er is s pu puzzli ling. ng.

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Mechanisms for uncommitted buyers with no positive transfers

Theorem: Interactive mechanism are necessary in

  • rder to get optimal revenue.
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Mechanisms for uncommitted buyers with no positive transfers

Theorem: Interactive mechanism are necessary in

  • rder to get optimal revenue.

$$ $$

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SLIDE 55

Mechanisms for uncommitted buyers with no positive transfers

How long can the protocol be ? How to optimize over interactive mechanisms ? How to do mechanisms design beyond the

  • ne-round revelation principle ?
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SLIDE 56

Mechanisms for uncommitted buyers with no positive transfers

How long can the protocol be ? How to optimize over interactive mechanisms ? How to do mechanisms design beyond the

  • ne-round revelation principle ?

?? ??

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SLIDE 57

How to design optimal interactive mechanisms ?

Open Problems

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How to design optimal interactive mechanisms ? Multiple buyers and sellers : a market for information

Open Problems

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How to design optimal interactive mechanisms ? Multiple buyers and sellers : a market for information Coupling goods and information

Open Problems

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How to design optimal interactive mechanisms ? Multiple buyers and sellers : a market for information Coupling goods and information Crypto primitives and computationally bounded agents

Open Problems

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How to design optimal interactive mechanisms ? Multiple buyers and sellers : a market for information Coupling goods and information Crypto primitives and computationally bounded agents Continuous type spaces

Open Problems