How to Bribe a Prison Guard and Applications

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

2. 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 iAGT Jerusalem

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 iAGT Hebrew University

4. Our mechanism for makespan Extends to many other problems • 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.   iAGT Jerusalem

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 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? NO iAGT Hebrew University

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

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? iAGT 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 iAGT 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 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 iAGT Hebrew University

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

13. Mechanism overview Lies, all lies iAGT Jerusalem

14. Mechanism overview Expected punishment for lying more than 1% on anyaij is greater than 100 times worst possible makespan (n H) Lies, all lies iAGT Jerusalem

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

16. Guards and Bribes • truecost • 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 iAGT Jerusalem

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

18. Bribes • true cost • Agent claims as cost of task • Prob: bribe: • Cost is • Truthful: iAGT Jerusalem

19. 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. iAGT Jerusalem

20. 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 : iAGT Jerusalem

21. Punishment for lying about the cost of the task • Cost of saying when truth is : • Punishment for saying when truth is : iAGT Jerusalem

22. Punishment for saying rather than iAGT Jerusalem

23. Thank you iAGT Hebrew University

24. Lying by a small factor • Other functions: iAGT Jerusalem

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

26. Ongoing and further work • Additive error vs multiplicative error • Can get such schemes from responsive lotteries, from scoring rules • Boccadellavarita 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? iAGT Jerusalem

27. Thank you iAGT Jerusalem