How to Bribe a Prison Guard and Applications
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Transcript of How to Bribe a Prison Guard and Applications
25/5/2011 iAGT Jerusalem
How to Bribe a Prison Guard and Applications
Amos Fiatjoint work with
Anna Karlin, Elias Koutsoupias, and Angelina Vidali
25/5/2011 iAGT Jerusalem
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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