Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Crm Esa08 1234869680124198 3

322 views

Published on

Published in: Technology, Design
  • Be the first to comment

  • Be the first to like this

Crm Esa08 1234869680124198 3

  1. 1. Collusion-Resistant Mechanisms with Verification Yielding Optimal Solutions Carmine Ventre (University of Liverpool) Joint work with: Paolo Penna (University of Salerno)
  2. 2. Routing in Networks s Change over time No Input (link load) Knowledge 3 10 1 1 2 Selfishness Private Cost 2 1 3 7 7 4 1 Internet
  3. 3. Mechanisms: Dealing w/ Selfishness s Augment an algorithm  3 with a payment function 10 1 1 The payment function  2 should incentive in 2 telling the truth 1 3 7 Design a truthful  mechanism 7 4 1
  4. 4. Truthful Mechanisms s M = (A, P) – cost = – true Utility = Payment M truthful if: , .... , ) ≥ Utility (bid, Utility (true, , .... , ) for all true, bid, and , ...,
  5. 5. Optimization & Truthful Mechanisms Objectives in contrast  Many lower bounds (even for two players and  exponential running time mechanisms) Variants of the SPT [Gualà&Proietti, 06]  Minimizing weighted sum scheduling [Archer&Tardos,  01] Scheduling Unrelated Machines [Nisan&Ronen, 99],  [Christodoulou & Koutsoupias & Vidali 07], … Workload minimization in interdomain routing [Mu’alem  & Schapira, 07], [Gamzu, 07] & a brand new computational lower bound  CPPP [Papadimitriou &Schapira & Singer, 08]  Study of optimal truthful mechanisms 
  6. 6. Collusion-Resistant Mechanisms CRMs are  “impossible” to achieve Coalition C Posted price  [Goldberg & Hartline, 05] Fixed output  [Schummer, 02] Unbounded apx  ratios ∑ Utility (true, true, , .... , ) ≥ ∑ Utility (bid, bid, , .... , ) + in C in C for all true, bid, C and , ..., –
  7. 7. Describing Real World: Collusions “Accused of bribery”  1,030,000 results on Google  1,635 results on Google news  Can we design CRMs using real-world information? 
  8. 8. Describing Real World: Verification TCP datagram starts at time  t Expected delivery is time t +  1… … but true delivery time is t  TCP 1 3 +3 It is possible to partially  verify declarations by observing delivery time Other examples:  Distance  Amount of traffic  Routes availability  IDEA ([Nisan & Ronen, 99]): No payment for agents caught by verification
  9. 9. Verification Setting Give the payment if the results are given “in  time” Agent is selected when reporting bid  true bid just wait and get the payment 1. true > bid no payment (punish agent ) 2.
  10. 10. CRMs w/verification for single- parameter bounded domains Agents aka as “binary” (in/out outcomes)  e.g., controls edges  Sufficient Properties  Pay all agents(!!!)  s Algorithm 32-resistant  true Truthfulness Pe’ = 0 10 true e 1 1 • e’ has no way to enter the 11+Pe 2 2 solution by unilaterally lying 2 true 1 • In coalition they 7can make the 10+Pe 10 3 e’ cut really expensive 7 4 true 1 Pe – 2 UtilityC(true)= UtilityC(bid)=Pbid – 10 ≥ 10 + Pe – 10 > UtilityC(true) true e’
  11. 11. Truthful Mechanisms w/ Verification: the threshold (A,P) truthful with verification A(bid, ) bid < in  ths in bid > out  ths out bid ths [Auletta&De Prisco&Penna&Persiano,04]
  12. 12. 2-resistant Algorithms b=(bid, bid, , .... , ) t=(true, true, , .... , ) bid ≥ true(Verification doesn’t work) b’ = b- =(bid , , .... , ) t’ = t- =(true , , .... , ) b’ t’ ≥ ths ths in out t’ b’ ths ths
  13. 13. Exploiting Verification: CRMs w/verification b’ h- if out ths Payment (b) = h if in (A,Payment) is a CRM Thm. Algorithm A 2-resistant w/ verification Proof Idea. At least one agent is caught by verification Usage of the constant h for bounded domains any number between bidmin & bidmax
  14. 14. b’ Proof (continued) h- if out ths Payment (b) = h if in Each is not worse No agent is caught by verification by truthtelling t b in in out in in out out in out out t’ b’ true true ths ths Utility (t) = h - true = Utility (b) Utility (t) = h - true ≥ h --trueb’ = Utility (b) t’ t’ b’ ≥h thsths ths ths
  15. 15. Simplifying Resistance Condition b=(bid, bid, , .... , ) b=(bid , , .... , ) t=(true, true, , .... , ) t=(true , , .... , ) bid ≥ true(Verification doesn’t work)≥ true bid b’ = b- b’ = b- =(bid , , .... , ) t’ = t- t’ = t- =(true , , .... , ) in Optimal b’ t’ CRMs ≥ thsout ths in t’ b’ ths ths Thm. Optimal threshold-monotone algorithms with out fixed tie breaking are n-resistant t’ b’ ths ths
  16. 16. Applications Optimal CRMs for:  MST  k-items auctions  Cheaper payments wrt [Penna&V,08]  Optimal truthful mechanisms for  multidimensional agents bidding from bounded domains and non-decreasing cost functions of the form Cost(bid , ..., bid )
  17. 17. Multidimensional Agents Outcomes = {X1, ..., Xm} View bid as a virtual coalition C bid =(bid(X1), .... ,bid(Xm)) of m single-parameter agents b=(bid , ..., bid ) B(b) optimal algorithm with A(bid ) m single-player fixed tie breaking rule functions P (b) = ∑ payment (bid ) in C Lemma. If every A is m-resistant then (B,P) is truthful Thm. For non-decreasing cost Every A is (B,P) is function of the form m-resistant truthful Cost(bid , ..., bid ) every A is threshold-monotone
  18. 18. Conclusions Optimal CRMs with verification for single-  parameter bounded domains Optimal truthful mechanisms for  multidimensional bounded domains Construction tight (removing any of the hypothesis we  get an impossibility result) Overcome many impossibility results by using a  real-world hypothesis (verification) For finite domains: Mechanisms polytime if  algorithm is Can we deal with unbounded domains? 

×