enforcing truthful-rating equilibria in electronic marketplaces t. g. papaioannou and g. d....
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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)
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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
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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.
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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
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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
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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
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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
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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
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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 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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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(
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Rr
RRr
Nr
rRRp
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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
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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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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
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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