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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. - PowerPoint PPT Presentation
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Optimal Collusion-Resistant Mechanisms with Verification
Carmine Ventre
Joint work with Paolo Penna
Routing in Networkss
12
310
2
1
1
4
37
71
Internet
Change over time (link load)
Private Cost
No Input Knowledge
Selfishness
d
Mechanisms: Dealing w/ Selfishness
Augment an algorithm with a payment function
The payment function should provide incentives for telling the truth
Design a truthful mechanism
s
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2
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d
d
Truthful Mechanisms
M = (A, P)
s
Utility (true, , .... , ) ≥ Utility (false, , .... , ) for all true, false, and , ...,
M truthful if:
Utility = Payment – cost = – true
VCG Mechanisms
M = (A, P)
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310
2
1
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71
Pe = Ae=∞ – Ae=0 if e is selected
(0 otherwise)
M is truthful iff A is optimal
Pe’ = Ae’=∞ – Ae’=0 = 7
e’Ae’=∞ = 14
Ae’=0 = 10 – 3 = 7
s
Utilitye’ = Pe’ – coste’ = 7 – 3
d
Inside VCG Payments
Pe = Ae=∞ – Ae=0
Cost of best solution w/o e
Independent from e
h(b–e)
Cost of computed solution w/ e = 0
Mimimum (A is OPT)
A(true) A(false)b–e all but e
Cost nondecreasing in the agents’ bids
Describing Real World: Collusions
Accused of bribery ~900,000 results on Google 6,463 results on Google news
Are VCGs collusion-resistant mechanisms?
Collusion-Resistant Mechanisms
Coalition C
+
–
∑ Utility (true, true, , .... , ) ≥ ∑ Utility (false,false, , .... , ) for all true, false, C and , ...,
in C in C
VCGs and Collusions
s
3
1
6e1
e2
e3
Pe1(true) = 6 – 1 = 5
e3 reported value
“Promise 10% of my new payment” (briber)
11
Pe1(false) = 11 – 1 – 1 = 9
“Pe3(false)” = 1
bribe
h( ) must be a constantb–e
d
Preventing Collusions is expensive Pay all the agents(!!!)
2
10
e
e’
Truthfulness
• 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)UtilityC(true)= Pe – 2
true
10+Petrue
11+Petrue
truePe’ = 0
UtilityC(false)=Pe’ – 10false ≥ 10 + Pe – 10 > UtilityC(true)true
s
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310
2
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37
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1
d
Constructing Collusion-Resistant Mechanisms (CRMs)
h is a constant function Pay all the agents A(true) A(false)
Coalition C
(A, VCG payments) is a CRM
How to ensure it? “Impossible” for classical mechanisms ([GH05]&[S00])
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
31TCP
IDEA ([Nisan & Ronen, 99]): No payment for agents caught by verification
The Verification Setting
Give the payment if the results are given “in time”
Agent is selected when reporting false1. true false just wait and get the payment 2. true > false no payment (punish agent )
Exploiting Verification: Optimal CRMs
No agent is caught by verification
At least one agent is caught by verification
A(true) = A(true, (t1, …, tn))
A(false, (t1, …, tn))
A(false, (b1, …, bn))
= A(false)
A is OPT
For any i ti bi
Cost is monotone
VCG hypotheses
Usage of the constant h for bounded domains
VCGs with verification are collusion-resistant
Any value between bmin e bmax
Approximate CRMs
Extending technique above: Optimize MinMax + AVCG
MinMax extensively studied in AMD E.g., Interdomain routing and Scheduling
Unrelated Machines Many lower bounds even for two players and
exponential running time mechanisms E.g., [NR99], [AT01], [GP06], [CKV07], [MS07], [G07],
[PSS08], [MPSS09]
MinMax objective functions admit a (1+ε)-apx CRM
Applications
* = FPTAS for a constant number of machines# = PTAS for a constant number of machines
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 polytime if algorithm is
Further Research
Frugality of payment scheme? Can we deal with unbounded domains? What is the real power of verification? Explore different definitions for the verification
paradigm [Nisan&Ronen, 1999] [Green & Laffont, 1986]...
... for which we can also look for untruthful mechanisms Apply verification to CAs