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How to Bribe a Prison Guard and Applications

Amos Fiatjoint work with

Anna Karlin, Elias Koutsoupias, and Angelina Vidali

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Major Motivating Example:Nisan & Ronen: STOC 1999

• m agents• n tasks• Goal: assign tasks to agents so that

all tasks done as soon as possible• Difficulty: agents lie about the time it

takes them to do task• Open problem: find incentive

compatible mechanism with good approximation

²This is a test²

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Other Solution Concepts?• Maybe the Nisan-Ronen problem (and others

“similar to it”) can be solved using long known techniques with [iteratively] undominated strategies? E.g., Abreu and Matsushima, Palfrey and

Srivastava, surveys by Jackson, Serrano, etc.• Does not work:

– Common knowledge (serious cheating)– No “Strict Value Distinction” (technical, but critical)– Less serious dirty tricks:

• Infinite sequences of undominated strategies, • Embedded Travelers Dilemma, etc

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Our mechanism for makespan

• Truthful in expectation• Probably, approximately, correct:

– With high probability, a approximation to the makespan

• I’m fudging: – Present or deal with (something) in a vague,

noncommittal, or inadequate way, esp. so as to conceal the truth or mislead.

– Adjust or manipulate (facts or figures) so as to present a desired picture.  

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Extends to many other problems

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Confluence of ideas

• Virtual Mechanisms• Probable approximate correctness• Scoring rules: encourage “best effort”

prediction • Responsive Lotteries• Undominated Strategies, Iteratively or not• Truthfulness in Expectation• Auctions using agent knowledge• Truthful mechanisms via differential

privacy25/5/

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How does Truth arise anyway?

Informer tells the Police– Either about the others

directly (common knowledge)

– Or, something about the others indirectly via own private data

– How do you make someone inform about herself?

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NO

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Bocca Della Verita• Early form of polygraph• Punishes liars • Appears in “Roman

Holiday” with Gregory Peck and Audrey Hepborn

Truth enforcing mechanisms• Devise mechanisms

that PUNISH you for lying.

• Goal: Punishment as painful as possible– As a function of what? – Additive error?

Multiplicative error?– Bounded range?

Infinite range? 25/5/2011 iAGT Jerusalem

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Basic Tool (Goods Formulation)

One stolen Greek vaseOne Mafioso bidderGOAL: Get good estimate of value to mafioso No priors, no eggplants

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Solution #17 ?• Let bidder make offer ( )• With probability give vase to

bidder, strictly monotonic increasing and concave, o.w., break vase

• Bidder chooses • Revelation principle, strictly

dominant to reveal – NOTE: Given , , we can compute

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We want more than Dominant Strategy Truthful

• One stolen Greek vase• One Mafioso bidder• Mafioso may have external

reasons to lie about true value

• We want to make it highly painful to lie about true value

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Use Example: Nisan-Ronen

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Agent 1: Agent 2:

TruthLies, all lies

Mechanism overview

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Lies, all lies

Mechanism overview

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Expected punishment for lying more than 1% on any aij is greater than 100 times worst possible makespan (n H)

Lies, all lies

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Implementing Truth Enforcing Mechanisms (Task Formulation)• true

cost of task (“work in salt mines”)

• Agent claims is true cost of task (possibly )

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Guards and Bribes• true cost • Agent claims as cost

of task • Agent (inmate) pays

prison guard bribe (in advance), function of

• Guard assigns task to agent with probability that depends on

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Bribes• true cost• Agent claims as cost of task• For any function

• Prob of assigning task to agent:

• Bribe to be paid

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Bribes• true cost• Agent claims as cost of task• Prob: bribe:

• Cost is

• Truthful:

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Optimal Truth Extraction Additive Lying

• true cost of task• Agent claims as cost of task • Take • Agent pays bribe (in advance):

• Agent assigned task w.p.

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Optimal Truth Extraction Additive Lying

• true cost of task• Agent claims as cost of task • Total cost to agent, if true cost is

and claimed cost is :

• Cost of saying when truth is :

• Punishment for saying when truth is :

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Punishment for lying about the cost of the task

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Punishment for saying rather than

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• Thank you

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Lying by a small factor• Other functions:

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We’re done• If agent lies too much (for any i,j):

then,

repeat punishment until it costs agent

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Ongoing and further work• Additive error vs multiplicative error• Can get such schemes from

responsive lotteries, from scoring rules

• Bocca della varita schemes for unbounded ranges?

• Punishment to fit the crime(s): – Strongly truthful GSP auction, prevent

strategy of using up opponents budget? – Strongly truthful combinatorial auctions? 25/5/2011 iAGT Jerusalem

Thank you

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