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 )]