Download presentation

Presentation is loading. Please wait.

Published byKarina Markwell Modified over 3 years ago

1
Collusion-Resistant Mechanisms with Verification Yielding Optimal Solutions Carmine Ventre (University of Liverpool) Joint work with: Paolo Penna (University of Salerno)

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

3
Mechanisms: Dealing w/ Selfishness Augment an algorithm with a payment function The payment function should incentive in telling the truth Design a truthful mechanism s 1 2 3 10 2 1 1 4 3 7 7 1

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

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
Collusion-Resistant Mechanisms CRMs are “impossible” to achieve Posted price [Goldberg & Hartline, 05] Fixed output [Schummer, 02] Unbounded apx ratios Coalition C + – ∑ Utility (true, true,,...., ) ≥ ∑ Utility (bid, bid,,...., ) for all true, bid, C and,..., in C

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
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 31 TCP IDEA ([Nisan & Ronen, 99]): No payment for agents caught by verification

9
Verification Setting Give the payment if the results are given “in time” Agent is selected when reporting bid 1. true bid just wait and get the payment 2. true > bid no payment (punish agent )

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(!!!) Algorithm 2-resistant s 1 2 3 10 2 1 1 4 3 7 7 1 2 e e’ Truthfulness e’ has no way to enter the solution by unilaterally lying In coalition they can make the cut really expensive Utility C (true)= P e – 2 true 10+P e true 11+P e true P e’ = 0 Utility C (bid)=P e’ – 10 bid ≥ 10 + P e – 10 > Utility C (true) true

11
Truthful Mechanisms w/ Verification: the threshold bid < in bid > out bid A(bid, ) (A,P) truthful with verification [Auletta&De Prisco&Penna&Persiano,04] ths in out ths

12
2-resistant Algorithms t=(true, true,,...., ) ths b’ ths t’ ≥ b’ = b=(bid, bid,,...., ) t’ = in out ths b’ ths t’ b - =(bid,,...., ) t - =(true,,...., ) bid ≥ true(Verification doesn’t work)

13
Exploiting Verification: CRMs w/verification At least one agent is caught by verification Usage of the constant h for bounded domains any number between bid min & bid max Payment (b) = h - if out ths b’ hif in Thm. Algorithm A 2-resistant (A,Payment) is a CRM w/ verification Proof Idea.

14
Proof (continued) in out ths b’ ths t’ No agent is caught by verification Each is not worse by truthtelling bt in out Utility (t) == Utility (b)h - true true Utility (t) = h - ≥ h - true ths t’ = Utility (b) Payment (b) = h - if out h if in ths b’ h - ≥ h - ths t’ ths b’ h - true ≥ h - ths b’ true

15
Simplifying Resistance Condition t=(true, true,,...., ) ths b’ ths t’ ≥ b’ = b=(bid, bid,,...., ) t’ = in out ths b’ ths t’ b - =(bid,,...., ) t - =(true,,...., ) bid ≥ true(Verification doesn’t work) b=(bid,,...., ) t=(true,,...., ) bid ≥ true b’ =b-b- t’ =t-t- in out ths b’ ths t’ Thm. Optimal threshold-monotone algorithms with fixed tie breaking are n-resistant Optimal CRMs

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
Multidimensional Agents Outcomes = {X1,..., Xm} bid =(bid(X1),....,bid(Xm)) b=(bid,..., bid ) B(b) optimal algorithm with fixed tie breaking rule A(bid ) m single-player functions View bid as a virtual coalition C of m single-parameter agents P (b) = ∑ payment (bid ) in C Lemma. If every A is m-resistant then (B,P) is truthful Thm. For non-decreasing cost function of the form Cost(bid,..., bid ) every A is threshold-monotone Every A is m-resistant (B,P) is truthful

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?

Similar presentations

OK

Mechanism Design. Overview Incentives in teams (T. Groves (1973)) Algorithmic mechanism design (Nisan and Ronen (2000)) - Shortest Path - Task Scheduling.

Mechanism Design. Overview Incentives in teams (T. Groves (1973)) Algorithmic mechanism design (Nisan and Ronen (2000)) - Shortest Path - Task Scheduling.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on student leadership Free ppt on mobile number portability vodafone Ppt on perimeter and area of circle Ppt on happy diwali Ppt on 2 stroke ic engine efficiency Download ppt on types of houses Water saving tips for kids ppt on batteries Ppt on marketing download Ppt on save water free download Ppt on blood stain pattern analysis books