trust based mechanism design by rajdeep dash, gopal ramchurn, nicholas jennings
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Trust Based Mechanism Design
By
Rajdeep Dash,
Gopal Ramchurn,
Nicholas Jennings
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Goal
Fuse the fields of trust-modelling and mechanism design
– Mechanism design concerns itself with the allocation of resources.
– Trust measures how good an interaction partner is according to personal experience and its reputation
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Deciding on a service provider
Garage X is better than Y
Garage Y is better than X!
1
2
Anna
Anna
Anna
Jo
Vanessa
3price3
price1
price2
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Motivation
Which garage to choose to get the best price AND my car repaired successfully?
1
2
Anna
3
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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 wants a task to be completed (e.g. repairing a car).
Problem – Who to allocate task to ? – How much to pay task performer ?
Solution - Vickrey Clarkes Groves (VCG) mechanism
- (e.g. second price (Vickrey) auction)
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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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Applying VCG
Centre
Ask(£80,repair_car)
(£210,repair_car)
Ask(£50,repair_car)
Allocate task to 1, 4 pays 1 £50
1
Anna (4)
Ask(£40,repair_car)
32
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Cheapest not always best …..
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Suppose that Anna has formulated a belief about the Probability of Success (POS), ,of other agents.
Adding uncertainties
Agent i
1 40 0.525 70.25
2 80 1.0 130
3 50 0.85 128.5
Ci
E[uA (K ;µA )]= vA ´iA ¡ ci
E[uA (K ;µA )]
´iA
´iA
E[uA (K ;µA )]
Chose allocation that maximises expected utility,
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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 one’s direct experience with the reputation information provided by others.
´iA
´ij
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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
Vanessa
2
Anna
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 23
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 ¤
Anna
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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 ; :)
Anna
Centre calculates optimal allocation without each agent i’s POS report. K¤¡ i
´i2c2 = 80´i1 c3 = 50
2 3
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TBMD
Centre(£210,task1)
Trust model
c1 = 40 ´i3
´i2c2 = 80´i1 c3 = 50
´i4
1
3
Centre calculates transfer to i , ri =mci ¡ Di
Anna
riK¤;
´i2c2 = 80´i1 c3 = 50
2 3
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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
Exp
ecte
d V
alu
e o
f A
llo
cati
on
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 Affords flexibility of context based trust modeling
with efficiency
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Our Case Study
Task Allocation– Some agents may perform some tasks
for which they incur a cost Ci– Others may ask for tasks to be performed
for which they have a valuation Vi– Eg. File-sharing on P2P networks, Selfish Multi-Sensor Nets
BUT there exists some uncertainty!– Agents may not perform tasks completely at times i.e. there
exists a probability of success (POS) in executing a task
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Trust-Based Mechanism
1. Find the optimal allocation given all trust reports
2. Find the optimal allocation with the trust report of each agent taken out in turn.
K¤ =argmaxK 2KP
i2 I [vi (K ;µi ) ¡ ci (K ;;µi )]
ti =P
i2 I nI [vi (K¤;µi ) ¡ ci (K ¤; ;µi )]¡
maxK 2KP
i2 I ni [vi (K ;µi ) ¡ ci (K ;;µi )]