Trust Based Mechanism Design

Use MD

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.

Deciding on a service provider

Garage X is better than Y

Garage Y is better than X!

X

Y

priceX

priceY

Motivation

WHICH GARAGE TO EMPLOY?

X

Y

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 4 wants a task to be completed.

• Problem – Who to allocate task to ? – How much to pay task performer ?

• Solution - VCG mechanism

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

• 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

Cheapest not always best …..

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)]

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

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

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 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

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

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¤;

Steps in TBMD

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

Expe

cted

Val

ue o

f Allo

catio

n

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.• Works with a very large class of trust models.

EndAny Questions?

rkd02r@ecs.soton.ac.uk