Trust Based Mechanism Design
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Transcript of Trust Based Mechanism Design
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Trust Based Mechanism Design
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Use MD
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Motivation
• Fuse the fields of trust-modelling and mechanism design
• Trust measures how good an interaction partner is
• Mechanism design concerns itself with the allocation of resources.
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Deciding on a service provider
Garage X is better than Y
Garage Y is better than X!
X
Y
priceX
priceY
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Motivation
WHICH GARAGE TO EMPLOY?
X
Y
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Mechanism Design
• The design of systems of interacting agents
– Protocols (allocation + payment schemes) to ensure that certain global properties are achieved at equilibrium (game-theoretic).
– Selfish, rational agents possessing private information i.e. each agent maximises its utility function given its type.
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Task Allocation
• Agent 4 wants a task to be completed.
• Problem – Who to allocate task to ? – How much to pay task performer ?
• Solution - VCG mechanism
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Applying VCG
Centre
Ask(£80,task1)
(£210,task1)
Ask(£50,task1)
Allocate task to 1, 4 pays 1 £50
1 2
4
Ask(£40,task1)
3
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• Class of mechanisms satisfying– Efficiency – outcome maximising utility for all
agents– Individually rationality – incentivise participation– Incentive compatibility – incentivise truthful report
under dominant strategy:• Works by:
– Allocation : choose allocation maximising utility– Payment : charge marginal utility contributed by
agent
VCG Mechanism
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Cheapest not always best …..
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Adding uncertainties
• Suppose that agent 4 has formulated a belief about the Probability of Success (POS) of other agents.
Agent i1 40 0.52
570.25
2 80 1.0 130
3 50 0.85 128.5
4 n/a n/a n/a
Ci ´i4 E[v4(K ;µ4)]
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Trust
• So far : one’s own experience. • Would be better to factor in others’
experiences as well.– First time agent– Greater pool of experience for seasoned user.
• Trust a way of aggregating everyone’s experience
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Our model of trust
• Each time a task is performed, record POS
• Publicly transmit the POS to other agents
• Trust– Use a simple averaging function
over reports from all agents– Give more weight to more
trusted referrals, or agents with similar properties
1
2
3
4
Record POS
Transmit POS
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Incorporate Trust
Agent i
1 40 0.4 1.0 0.85 0.5 65
2 80 0.6 1.0 0.9 1.0 130
3 50 0.5 1.0 0.9 0.87 132.7
4 0.525 1.0 0.85 na na
´1i ´2i ´3i
1
ti4 E[v4(j ;µ4)]
®= [0:3 0:2 0:1 0:4]; v4(¿) = 210
ci
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TBMD
Centre
(£210,task1)Trust model
c1 = 40 ´i3
´i2c2 = 80´i1 c3 = 50
´i4
1 2
3
4 transmits to centre -- value of task, observed POS and trust model1, 2, 3 transmit to centre -- cost of doing task and observed POSCentre calculates optimal allocation bK ¤
4
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TBMD
Centre
(£210,task1)Trust model
c1 = 40 ´i3
´i2c2 = 80´i1 c3 = 50
´i4
1 2
3
Di =U( bK ¤; :) ¡ U(K ¤¡ i ; :)
4
Centre calculates optimal allocation without each agent i’s POS report. K¤¡ i
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TBMD
Centre
(£210,task1)Trust model
c1 = 40 ´i3
´i2c2 = 80´i1 c3 = 50
´i4
1 2
3
Centre calculates transfer to i , ri =mci ¡ Di
4
riK¤;
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Steps in TBMD
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Trust Based Mechanism Design (TBMD)
• An individually rational and efficient ICDR mechanism that can also select those agents that are most successful at their task
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Experimental Setup
• Set of buyers and sellers. • Biased (but truthful!) report from seller.• Buyers attach different levels of
importance to seller’s report.
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Results
0.75
0.8
0.85
0.9
0.95
1
1 101 201 301 401 501
Iteration
Expe
cted
Val
ue o
f Allo
catio
n
K*FTM
K*TBM0.5
K*VCG
K*
K*TBM0.25
K*TBM
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Conclusions
• Task allocation with uncertainty.• Only incentive-compatible, individually-rational
efficient reputation mechanism.• Works with a very large class of trust models.