1. 25/5/2011iAGT Jerusalem How to Bribe a Prison Guard and Applications Amos Fiat joint work with Anna Karlin, Elias Koutsoupias, and Angelina Vidali TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA

2. 25/5/2011iAGT 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

3. 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 25/5/2011iAGT Hebrew University

4. 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. 25/5/2011iAGT Jerusalem Extends to many other problems

5. 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 privacy 25/5/iAGT Hebrew University

6. 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? 25/5/2011iAGT Hebrew University

7. 25/5/2011iAGT Jerusalem Bocca Della Verita Early form of polygraph Punishes liars Appears in “Roman Holiday” with Gregory Peck and Audrey Hepborn

8. 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? 25/5/2011iAGT Jerusalem

9. Basic Tool (Goods Formulation) One stolen Greek vase One Mafioso bidder GOAL: Get good estimate of value to mafioso No priors, no eggplants 25/5/2011iAGT Hebrew University

10. 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 25/5/iAGT Hebrew University

11. 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 25/5/2011iAGT Hebrew University

12. Use Example: Nisan-Ronen 25/5/2011iAGT Jerusalem Agent 1: Agent 2: Truth Lies, all lies

13. Mechanism overview 25/5/2011iAGT Jerusalem Lies, all lies

14. Mechanism overview 25/5/2011iAGT Jerusalem Expected punishment for lying more than 1% on any a ij is greater than 100 times worst possible makespan (n H) Lies, all lies

15. 25/5/2011iAGT Jerusalem Implementing Truth Enforcing Mechanisms (Task Formulation) true cost of task (“work in salt mines”) Agent claims is true cost of task (possibly )

16. 25/5/2011iAGT Jerusalem 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

17. 25/5/2011iAGT Jerusalem Bribes true cost Agent claims as cost of task For any function Prob of assigning task to agent: Bribe to be paid

18. 25/5/2011iAGT Jerusalem Bribes true cost Agent claims as cost of task Prob: bribe: Cost is Truthful:

19. 25/5/2011iAGT Jerusalem 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.

20. 25/5/2011iAGT Jerusalem 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 :

21. Cost of saying when truth is : Punishment for saying when truth is : 25/5/2011iAGT Jerusalem Punishment for lying about the cost of the task

22. 25/5/2011iAGT Jerusalem Punishment for saying rather than

23. Thank you 25/5/2011iAGT Hebrew University

24. Lying by a small factor Other functions: 25/5/2011iAGT Jerusalem

25. We’re done If agent lies too much (for any i,j): then, repeat punishment until it costs agent 25/5/2011iAGT Jerusalem

26. 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? 25/5/2011iAGT Jerusalem

27. Thank you 25/5/2011iAGT Jerusalem

28. Annoying Results on Approximation Bounds For deterministic mechanisms: For truthful in expectation mechanisms: For anonymous mechanisms: For two values: 25/5/2011iAGT Jerusalem [KV], [NR] [CKK] [ADL] [LS] (Sort of)