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Trust Based Mechanism Design
By
Rajdeep Dash,
Gopal Ramchurn,
Nicholas Jennings
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
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
Motivation
Which garage to choose to get the best price AND my car repaired successfully?
1
2
Anna
3
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.
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)
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
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
Cheapest not always best …..
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,
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
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
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
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
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
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
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
Experimental Setup
Set of buyers and sellers. Biased (but truthful!) report from seller. Buyers attach different levels of importance to seller’s
report.
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
Conclusions
Task allocation with uncertainty Only incentive-compatible, individually-rational
efficient reputation mechanism Affords flexibility of context based trust modeling
with efficiency
End
Any Questions?rkd02r@ecs.soton.ac.uk
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
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 )]
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