Enforcing Truthful-Rating Equilibria

in Electronic Marketplaces

T. G. Papaioannou and G. D. Stamoulis

Networks Economics & Services Lab, Dept.of Informatics,

Athens Univ. of Economics & Business (AUEB) http://nes.aueb.gr

“Towards a Science of Networks” WorkshopSounion, Greece – September 1, 2006

Work partly funded by EuroNGI Network of Excellence (IST-2003-507613)

2

Overview

Problem definition and related work

The basic model and its analysisfixed punishments

The extended model and its analysisreputation-based punishments

Conclusions – Recent and Future Work

3

Reputation in Peer-to-Peer Systems Reputation reveals hidden information about peers Is only effective with reputation-based policies [1]

“Provider Selection” and “Contention Resolution” policies But, reputation is vulnerable to false/malicious ratings Collect ratings on each transaction from both parties and

punish both in case of disagreement [2]At least one of them is lyingPunishment is not monetary bans participation for some time

[1] “Reputation-based policies that provide the right incentives in peer-to-peer environments”, Computer Networks, vol. 50, no. 4, March 2006.[2] “An Incentives' Mechanism Promoting Truthful Feedback in Peer-to-Peer Systems”, GP2PC’05.

4

The New Context Reputation is now studied in electronic

marketplaces where participants actboth as providers and as clients competitively, so as to maximize their market share

Applications: exchanging of vinyl records among collectors, software modules among programmers, news among agencies, etc.

Provider selection is based on reputation

Malicious rating offers future competitive advantage

5

Objective & Contribution

Objective: Provide incentives for truthful ratings by

participants in the new context

Contribution: Analyzed the dynamics of fixed monetary

punishments Derived necessary conditions for stable truthful

rating equilibrium Customized punishments w.r.t. reputation to limit

social unfairness

6

Related Work: Monetary-Penalty Approaches

Miller, Resnick, Zeckhauser: Truthful rating is a Nash equilibrium for clients if certain penalties are imposed to them upon evidence of lying

Jurca, Faltings: Side-payments imposed upon evidence of lying. Clients are truthful and do not act as providers

Dellarocas: Penalty to provider to compensate payoff gains from offering lower quality than promised. Nash equilibrium for truthful clients

7

Innovation in this Research

Dual role of participants

Reputation-based competition and its impact on incentives for reporting truthful ratings

Stability analysis of truthful-rating Nash equilibrium enforced by each mechanism

Tailored reputation-based punishments

8

The Basic Model

9

Providers and Clients

E-marketplace with N participantsN is either fixed or mean number of

participants with geometrically distributed lifetimes

Time is partitioned in roundsDuring a round:

Each participant acts:– either as a provider with probability q – or as a client with probability 1-q

One client is selected at random to be served

10

Selecting a Provider

Reputation-based policy: A clients selects the provider to associate with in a probabilistically fair manner w.r.t. the reputation of the latterA provider i is selected during a round with probability proportional to his rank

Each participant has a probability ai to provide a service instance successfully, with satisfactory quality ai is private information, estimated by reputation

– e.g. percentage of past successful provisions

r

rR i

i

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Costs, Payments, Ratings A successfully provided service instance:

Offers fixed utility u to the clientDemands costly effort v by the provider Costs b to the client

A pre-payment p·b is paid for each service to balance the risks

Both transacted parties submit a binary rating of the service providedUpon agreement, the client pays (1-p)·b and the vote

is registered for updating the provider’s reputationUpon disagreement a fixed punishment c is imposed

to both

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Single-Transaction Game Two sub-games depending on the outcome of the

service provision: success or failure

Set of Reporting strategies: S = {Witness, Lie, Duck}

Impact of agreed rating to future payoffs of participantsA positive rating results in payoff impact wp > 0 for the

provider and -wc < 0 for the client

A negative rating results in payoff impact -wp < 0 for the provider and wc > 0 for the client

Payoff impacts are taken independent of current reputation

~~

u-b-wc

b-v+wp

u-p·b-c

p·b-v-c

u-p·b-c

p·b-v-c

u-b-c

b-v-c

u-p·b+wc’

p·b-v-wp’

u-p·b-c

p·b-v-c

u-b-c

b-v-c

u-p·b-c

p·b-v-c

u-p·b

p·b-v-p·b+wc’

p·b-wp’

-p·b-c

p·b-c

-p·b-c

p·b-c

-p·b-c

p·b-c

-p·b-wc

p·b+wp

-p·b-c

p·b-c

-p·b-c

p·b-c

-p·b-c

p·b-c

-p·bp·b

clientprovider

success

failure

ai

1-ai

Witness

Witness Lie

Lie

Duck

Duck

Witness

Lie

Duck

~

~

~

~

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Truthful-Rating Equilibriumunder the Basic Model

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Truthful Nash Equilibrium Derive conditions for disagreement punishment c so

that truthful rating is a Nash equilibrium in both sub-games

Disagreement may rationally arise only in two casesSuccess: provider Witness and client Lie or DuckFailure: client Witness and provider Lie or Duck

Witness is best response to itself when c > (1-p)·b+wc and c > wp

Does this equilibrium indeed arise ? Is it stable ?

~

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Evolutionary Stability

Evolutionary Stable Strategy (ESS):1. Nash equilibrium2. Is a better reply to any mutant strategy than

the latter is to itself

Strict Nash equilibrium of the asymmetric game ESS of its symmetric version

Evolutionary dynamics for strategy s with payoff πs played by a population fraction xs:

)( sss

s xdt

dxx

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Stable Truthful Rating

(x1, x2, x3) are the population fractions of providers that play Witness, Lie, Duck in the success sub-game

(y1, y2, y3) are these fractions for clients

Basin of attraction of truthful-rating equilibrium:Region for population mix that ultimately

leads all participants to play Witness

(x1, x2, x3) = (1,0,0) and (y1, y2, y3) = (1,0,0)

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The Basin of Attraction of Truthful Rating

Success sub-game X Y

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The Basin of Attraction of Truthful Rating

Failure sub-game X’ Y’

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The Extended Model

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Differences from Basic Model

Disagreement punishment is not fixedDepends on the transacted participant’s:

– Rank, i.e. reputation– Role

which are public information

Payoff impacts of a vote wp , -wc , wp , -wc are not taken fixedCalculated explicitly

~ ~

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Innovative Reputation Metric

Beta reputation metric:

Results to time-dependent impact of a single vote to rank values of transacted parties

Solution: An innovative reputation metric

Still provides the right incentivesNow, rank impacts are not time-dependent; e.g.

1

)success(

n

zr

1

)1)(success( 1rr

)1

)(1()1)(1(

11

Rr

RRr

Nr

rRRp

23

Reputation-based Punishments

Derived conditions for disagreement punishments that enforce the truthful-rating equilibrium

Outline of Proof Necessary and sufficient condition:A single-round deviation from truthful rating

at round t is not beneficial.

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)])(1()([1

])1()([1

),( )()(

pbabuaN

pbavbaRN

aRV iit

iit

i

Some Algebra Expected payoff for a participant i at round t :

After a non-truthful rating at round t, future ranks of participant i are Calculated explicitly, separately for provider and for client

rank success probability

mean success probability

,...~

,~ )2()1( t

it

i RR

payoff as client

payoff as provider

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The Conditions on Punishments Provider’s punishment:

pt

iiiitt

ip waRVaRVRf ~)],(),~

([)(1

)()()(

Client’s punishment:

Since N is large, fp is approximated by a simple formula

This is bounded from above and below

ct

iiiitt

ic wbpaRVaRVbpRf

)1()],(),~

([)1()(1

)()()(

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2 4 6 8 10

0.002

0.004

0.006

0.008

0.01

0.012

Numerical Example

N=50, q=0.4, p=0.2, b=2, u=2.5, v=0.5, =0.6, =0.9R

Disagreement Payoff Impactwp(R), wc(R)

ProviderClient

Punishment for Disagreement

R

~

2 4 6 8 10

0.25

0.5

0.75

1

1.25

1.5

27

Social Benefit Estimation

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Social Loss

Disagreement punishment is unfairly induced to one of the transacted participants social loss

When punishment is fixed, c > q wp + (1-q)[(1-p)b+wc]The maximum payoff impacts wp , wc have to be assumed

Thus, unfairness is induced for all the non-highest ranked participants greater social loss

Reputation-based punishments eliminate this unfairness!

~~

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Numerical Example

Normal distribution of ranks with (μ, σ)=(1, 0.5)

Social benefit: Ratio of average reputation-based punishment over fixed punishment for various mean-reputation values of the population

Population’s mean-reputation

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Reputation-based Punishment Fixed Punishment

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Concluding Remarks

31

Summary of our Contribution

Proposed a simple mechanism that provides incentives for truthful rating in an interesting context of an e-marketplaceReputation-based competitionDual role of participants

Derived conditions on the effectiveness of such a mechanism with fixed punishmentsStability analysis of truthful-rating Nash equilibrium

Derived tailored reputation-based punishmentsSignificant reduction of social loss

32

Recent and Future Work

Employ different fixed punishments for provider and client

Consider the success probability of each participant as a strategic parameter, rather than as being fixed

Derive upper bound for the social loss reduction with reputation-based disagreement punishments

Explore stability conditions for truthful equilibrium with reputation-based disagreement punishments