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Optimal Collusion-Resistant Mechanisms with Verification

Optimal Collusion-Resistant Mechanisms with Verification. Carmine Ventre Joint work with Paolo Penna. Routing in Networks. s. Change over time (link load). No Input Knowledge. 3. 10. 1. 1. 2. Selfishness. Private Cost. 2. 1. 3. 7. 7. 4. 1. d. Internet.

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Optimal Collusion-Resistant Mechanisms with Verification

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  1. Optimal Collusion-Resistant Mechanisms with Verification Carmine Ventre Joint work with Paolo Penna

  2. Routing in Networks s Change over time (link load) No Input Knowledge 3 10 1 1 2 Selfishness Private Cost 2 1 3 7 7 4 1 d Internet

  3. Mechanisms: Dealing w/ Selfishness s • Augment an algorithm with a payment function • The payment function should provide incentives for telling the truth • Design a truthful mechanism 3 10 1 1 2 2 1 3 7 7 4 1 d

  4. M = (A, P) Truthful Mechanisms s Utility = Payment – cost = – true M truthful if: d Utility (true, , .... , ) ≥ Utility (false, , .... , ) for all true, false, and , ...,

  5. M = (A, P) VCG Mechanisms Pe’ = Ae’=∞ – Ae’=0 = 7 Ae’=∞ = 14 s e’ 3 Ae’=0 = 10 – 3 = 7 10 1 1 2 2 1 3 7 4 7 1 d Pe = Ae=∞ – Ae=0 if e is selected (0 otherwise) Utilitye’ = Pe’ – coste’ = 7 – 3 M is truthful iff A is optimal

  6. Inside VCG Payments Cost nondecreasing in the agents’ bids Pe = Ae=∞ – Ae=0 Cost of computed solution w/ e = 0 Cost of best solution w/o e Mimimum (A is OPT) Independent from e h(b–e) A(true)  A(false) b–e all but e

  7. Describing Real World: Collusions • Accused of bribery • ~900,000 results on Google • 6,463 results on Google news • Are VCGs collusion-resistant mechanisms?

  8. Collusion-Resistant Mechanisms ∑ Utility (true, true, , .... , ) ≥ ∑ Utility (false,false, , .... , ) for all true, false, C and , ..., in C in C Coalition C + –

  9. VCGs and Collusions e3 reported value Pe1(true) = 6 – 1 = 5 s Pe1(false) = 11 – 1 – 1 = 9 3 e3 e1 11 6 “Pe3(false)” = 1 bribe 1 e2 d h( ) must be a constant b–e “Promise 10% of my new payment” (briber)

  10. Preventing Collusions is expensive s • Pay all the agents(!!!) 3 10 1 1 2 • e’ to enter the solution by unilaterally lying must underbid (competition, i.e., non-cooperative behaviour) • In coalition they can make the cut really expensive (cooperative behaviour) Truthfulness 2 true true 10+Pe 11+Pe 1 e 2 3 7 d true 10 Pe’ = 0 7 e’ 4 1 false true UtilityC(false)=Pe’ – 10 ≥ 10 + Pe– 10 > UtilityC(true) true UtilityC(true)= Pe – 2

  11. Constructing Collusion-Resistant Mechanisms (CRMs) • h is a constantfunction • Payall the agents • A(true)  A(false) Coalition C (A, VCG payments) is a CRM How to ensure it? “Impossible” forclassicalmechanisms ([GH05]&[S00])

  12. Describing Real World: Verification • TCP datagram starts at time t • Expected delivery is time t + 1… • … but true delivery time is t + 3 • It is possible to partially verify declarations by observing delivery time • Other examples: • Distance • Amount of traffic • Routes availability TCP 3 1 IDEA ([Nisan & Ronen, 99]): No payment for agents caught by verification

  13. The Verification Setting • Give the payment if the results are given “in time” • Agent is selected when reporting false • truefalse just wait and get the payment • true>false no payment (punish agent )

  14. VCGs with verification are collusion-resistant Exploiting Verification: Optimal CRMs For any i ti bi No agent is caught by verification A(true) = A(true, (t1, …, tn)) A is OPT  A(false, (t1, …, tn)) Costis monotone  A(false, (b1, …, bn)) VCG hypotheses = A(false) At least one agent is caught by verification Usage of the constant h for bounded domains Anyvaluebetweenbmin e bmax

  15. MinMax objective functions admit a (1+ε)-apx CRM ApproximateCRMs • Extendingtechniqueabove: OptimizeMinMax + AVCG • MinMax extensively studied in AMD • E.g., Interdomain routing and SchedulingUnrelatedMachines • Manylowerboundsevenfortwoplayers and exponentialrunningtimemechanisms • E.g., [NR99], [AT01], [GP06], [CKV07], [MS07], [G07], [PSS08], [MPSS09]

  16. Applications * = FPTAS for a constant number of machines # = PTAS for a constant number of machines

  17. Conclusions • Collusion-Resistant mechanisms with verification for arbitrary bounded domains optimizing generalization of utilitarian (VCG) cost functions • Overcome many impossibility results by using a real-world hypothesis (verification) • Efficient Mechanisms • Mechanism is polytimeif algorithm is

  18. Further Research • Frugality of payment scheme? • Can we deal with unbounded domains? • Whatis the realpowerofverification? • Explore different definitions for the verification paradigm • [Nisan&Ronen, 1999] • [Green & Laffont, 1986]... • ... for which we can also look for untruthful mechanisms • ApplyverificationtoCAs

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