efficiency and robustness of binary online feedback...

Efficiency and Robustness of Efficiency and Robustness of Binary Online Feedback Mechanisms in Binary Online Feedback Mechanisms in

Trading Environments with Moral HazardTrading Environments with Moral Hazard

Chris Dellarocas

MIT Sloan School of Management

[email protected]

OutlineOutline

• Introduction and Motivation

• The model: Binary feedback mechanisms in settings with moral hazard

• Derivation of equilibrium play and payoffs

• Robustness analysis

• Relationship to empirical findings

• Extensions and future work

What are online reputation mechanisms?What are online reputation mechanisms?

• Online “word-of-mouth networks” induced and controlled by information technology

• Solicit, aggregate and publish “opinions” from members of an online community

• Harness one of the truly new capabilities of the Internet relative to all past technologies for mass communication

• Examples:

– eBay– Epinions– Google– …

Why are online feedback mechanisms Why are online feedback mechanisms interesting?interesting?

So far…

• Promising alternative to more traditional quality assurance mechanisms in environments where state enforcement does not work as well (e.g. electronic markets)

In the near future…

• Fundamentally change the dynamics between corporations and individuals (government and citizens???)

• Example: Intel Pentium Floating Point Bug

• Implications for

– Brand creation/sustenance– Customer acquisition/retention– Public opinion formation

How do they differ from traditional How do they differ from traditional wordword--ofof--mouth networks?mouth networks?

• The Internet allows unprecedented scalability

• Information technology enables precise design and control• What information is solicited from community members• How it is aggregated/filtered/weighted• What information is disseminated to members about other

members• ….

• Online interaction introduces new challenges• Subjective opinions• Fake identities• Unqualified raters• Untruthful feedback• …

An emerging research agendaAn emerging research agenda

• Identify settings where such mechanisms can be useful

• Explore the design space of such mechanisms

– What type of feedback should be solicited?– How should it be aggregated?– What type of feedback profiles should be published?– What should be the incentives for participation/truth-telling?– …

• Understand what designs are best for what settings in terms of efficiency, robustness, etc.

• Compare reputation mechanisms with other institutions that aim to achieve similar goals

• …

Today’s talkToday’s talk

• Explore the design space of reputation mechanisms for trading environments with:

– Monopolist sellers– Two effort levels/two outcomes (high/low quality)– Imperfect monitoring (moral hazard)

• Study the equilibria induced by a family of mechanisms that resemble the one used by eBay

• Examine the impact of a number of design parameters on efficiency

• Study the robustness of these mechanisms to incomplete feedback submission and easy identity changes

The modelThe model

The settingThe setting

• One long-term monopolist seller

• Many competing one-time buyers

• In each round, the seller auctions a single unit of a product/service (Vickrey auction assumed)

• Two possible qualities of product/service; low quality is unacceptable to all buyers

– e.g., fake or never shipped good, substandard service

• Two possible seller effort levels: high effort costs c and results in low quality with probability α; low effort costs zero but results in low quality with probability β>α

• Private perception of quality by buyers

A single round of the gameA single round of the game

1. Buyers decide how much to bid taking into account seller’s feedback profile

2. Winning buyer makes payment to seller

3. Seller decides high/low effort level

4. Buyer privately perceives quality and posts rating (positive/negative) for seller

5. Feedback mechanism updates seller’s profile

“Binary” feedback mediators“Binary” feedback mediators

• Solicit binary feedback (positive/negative ratings)

• Publish an approximate count x of negative ratings received during the N most recent periods

• More specifically:

– Mediator maintains an unordered set Q of N recent reports.At the end of each stage game: – Let r be the current report submitted by the buyer – Randomly select a report in Q and replace it with r– Recalculate and publish the new sum x of negative reports in Q

• If N is fixed then the profile is simply characterized by the state variable x∈{0,...,Ν}

Binary feedback mediator design parametersBinary feedback mediator design parameters

• N Number of recent reports “summarized” in profile x

• x0 Initial profile state of new sellers, x0 ∈{0,...,Ν}

Equilibrium play and payoffsEquilibrium play and payoffs

PreliminariesPreliminaries• Seller’s stage-game action space:

– Cooperate=exert high effort– Cheat=exert low effort

• Let s(x,H) be the seller’s probability of cooperation if his current profile is x and the game’s past history is H

• We will only consider stationary strategies s(x)– Will later show that seller can do no better by considering the full set of

strategies s(x,H)

• Let be the seller’s strategy vector

• Buyers’ action space includes all possible bid amounts; since buyers are short-term they play a static best-response to the seller’s strategy

• Seller’s objective is to maximize his payoff

[ ])(),...,0( Nss=s

0[ ( )]t

st

V E h tδ∞

=

= ⋅∑)(th

s is the seller’s stage-game payoff at time t

Equilibrium strategy resulting in maximum Equilibrium strategy resulting in maximum payoffs (Proposition 3.1)payoffs (Proposition 3.1)

• Equilibrium strategy that results in maximum payoff depends on the ratio

– Rough measure of the profit margin of cooperating sellers

• Case I (inefficient case): If the feedback

mechanism fails to induce cooperation:

2 /w cρ =

],...,0,0)([* Nxxs ===s

2( )

βρ

δ β α<

⋅ −

2( ) (1 )G x wβ= − ⋅ 2(1 )

1

wV

β

δ

−=

−

Proposition 3.1: (cont’d)Proposition 3.1: (cont’d)

• Case II (“efficient case”): If the

feedback mechanism induces mixed strategies with prob.

of cooperation linearly decreasing with the number of

negatives in the seller’s profile

2(1 )

( )Nδ δρ

δ β α+ −

≥⋅ −

* 22

/[ ( ) 1 (1 ) , 0,..., ]( )c ws x x x N

Nδδ

δ β α= = − ⋅ − + ⋅ =

⋅ −sseller

strategy

2( ) (1 ) (1 )( )

cG x w xNδα δ

δ β α= − − ⋅ − + ⋅

⋅ −auctionrevenue

where x0 is a new seller’s initial feedback profile state

0 2 01( ) (1 )

1 ( )c cV x w c xαα

δ β α δ β α ⋅

= − − − − ⋅ − − ⋅ − payoff

Example:Example:• α=0.1, β=1- α , δ=0.999, ρ=2, c=1, N=30

• Average x=8.42 Average cooperation=0.774

0

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0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Number of negative ratings (x)

Prob

. of c

oope

ratio

n s(

x)

0

0.01

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Stat

iona

ry p

rob.

of s

tate

x

s(x) Stationary probabilities



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. of c

oope

ratio

n s(

x)

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rob.

of s

tate

x




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oope

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n s(

x)

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iona

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rob.

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Efficiency considerationsEfficiency considerations• Even cooperating sellers will eventually receive negative

ratings and will transition to states of less than perfect cooperation

• This results in efficiency loss relative to the first-best case (cooperate always)

• Highest payoffs attainable when new sellers are started with a “clean record” (x0=0)

• Can another mechanism do better?– More specifically, would it help to provide the entire history

of feedback?

21(0) (1 )

1cV w c αα

δ β α ⋅

= − − − − −

Efficiency loss relative to first-best

Efficiency of binary feedback mechanismsEfficiency of binary feedback mechanisms

• Proposition 3.2: The set of sequential equilibrium seller payoffs (i.e those attainable by both public and private seller strategies) of a repeated game with the stage game structure described previously and where the entire public history of buyer reports is available to short-run players is bounded above by

• Proof: Based on the maximal score method of Fudenbergand Levine (1994) for computing the feasible payoffs of repeated games with long-run and short-run players

*2

1 (1 )1

cV w c ααδ β α ⋅

= − − − − −

Corollary: Maximum payoffs are Corollary: Maximum payoffs are independent of independent of NN

• Obvious, because formula for V(0) does not involve N

• Simplest mechanism for N=1: simply publish the single most recent rating

• Above result means that an eBay-like mechanism that publishes the single most recent rating induces maximum payoffs equal to a mechanism that publishes the entire feedback history

• Interesting indication of the power of mediated feedback to simplify decision making without sacrificing efficiency

Robustness analysisRobustness analysis

Robustness analysisRobustness analysis

• Incomplete feedback submission

• Strategic name changes

Issue 1: Incomplete feedback submissionIssue 1: Incomplete feedback submission

• Assume that not every buyer submits feedback

• More specifically

– If a buyer perceives high quality she submits (positive) feedback with probability η+ , no feedback otherwise

– If a buyer perceives low quality she submits (negative) feedback with probability η - , no feedback otherwise

– η + , η - exogenous

Missing feedback policiesMissing feedback policies

• Policy 1: Treat missing feedback as positive feedback

• Policy 2: Treat missing feedback as negative feedback

• Policy 3: Ignore transactions for which no feedback has been provided (this is the current policy of eBay)

Results: Which policy is best?Results: Which policy is best?

• Efficiency(Policy 1) ≥ Efficiency(Policy 2)

– Equality only if η+ =1

• Efficiency(Policy 1) ≥ Efficiency(Policy 3)

– Equality only if η+ = η-

• Corollary:

– A “no news is good news” policy induces maximum efficiency

Results: How does incomplete feedback Results: How does incomplete feedback submission affect efficiency?submission affect efficiency?

• Under a “no news is good news” policy

– Incomplete feedback submission increases the threshold ρrequired in order for the mechanism to induce cooperation by a factor 1/ η-

– If the profit margins are high enough to satisfy the new threshold ρ, the maximum seller payoff (for x0=0) is independent of the probability of feedback submission

– Incomplete feedback submission thus has less severe consequences than previously thought

Issue 2: Strategic name changesIssue 2: Strategic name changes

• Assume that new identity acquisition/re-entry are free

• Sellers can then disappear and reappear with a new identity whenever their feedback profile becomes too unfavorable

• First discussed by Friedman and Resnick (2001)

• In our model, sellers will disappear whenever they transition to a state x with lower payoff than that of the initial state x0 of new sellers

• If x0=0, since seller payoff linearly decreases with x, seller would disappear as soon as he got a single negative, which gives him no incentive to cooperate. Seller would cheat always.

Preventing strategic name changesPreventing strategic name changes

• Set initial state of newcomer sellers equal to x0=N

• This corresponds to the state with lowest payoffs. There is never an incentive to disappear and reappear.

• Newcomer sellers would then “start low” and gradually transition to states with fewer negatives and higher payoffs

Efficiency implications of Efficiency implications of easy name changeseasy name changes

• If the absence of this issue, the most efficient initial state would have been x0=0, resulting in payoff

• If cheap pseudonyms are a concern, setting x0=N reduces the seller’s lifetime (normalized) payoff to

• Note that efficiency loss is minimized when N=1: the simplest binary feedback mechanism is also the most robust in the presence of easy name changes!

21(0) (1 )

1cV w c αα

δ β α ⋅

= − − − − −

21( ) (1 )

1 ( )c cV N w c Nαα


= − − − − ⋅ − − ⋅ −

A general resultA general result

• Proposition 4.3: If players can costlessly change identities, the set of sequential equilibrium seller payoffs of a repeated game with the stage game structure described in this talk and where the entire public history of buyer reports is available to short-run players is bounded above by

• Corollary: Binary feedback mechanisms with N=1, x0=1constitute the “optimal” solution to the problem of easy name changes

21 (1 )

1 ( )c cw c αα


− − − − − − ⋅ −

Relationship to empirical findingsRelationship to empirical findings

Model calibrationModel calibration

• In online environments, there is relatively little noise (probability of low quality if seller exerts high effort)

• Therefore, let α=0.01, β=1- α

• Empirical data suggests that feedback submission on eBay is about 50%

• Let η+ = η- = 0.5

• A striking property of eBay is the very low fraction of negative feedback (less than 1%)

Maximum efficiency (relative to firstMaximum efficiency (relative to first--best)best)

• Threshold for most efficient equilibrium to obtain

0.75

0.8

0.85

0.9

0.95

1

1.05 1.2 1.35 1.5 1.65 1.8 1.95 2.1 2.25 2.4

rho

Rela

tive

effic

ienc

y1.04ρ ≥

Frequency of negative feedbackFrequency of negative feedback• For α=0.01, β=1- α, only 0.98% of submitted feedback is expected to

be negative

• Consistent with empirical observations

0

0.01

0.02

0.03

0.04

0.05

0 0.01 0.02 0.03 0.04 0.05

alpha

Expe

cted

frac

tion

of n

egat

ive

feed

back

Conclusions and future workConclusions and future work

Contributions of this paperContributions of this paper

• Theoretical

– Efficiency is independent of N– Optimal policy in the presence of incomplete feedback

submission is “no news is good news”– Study of the impact and solution to the problem of easy

name changes

• Practical

– Theoretical predictions consistent with empirical findings– Suggestions for improving eBay’s mechanism

• Consider fixing N (to a small value)• Change policy for missing feedback• Start new sellers with a “bad” reputation to prevent strategic

name changes

Extensions of the modelExtensions of the model

• Multiple sellers: feedback mechanisms in competitive environments

• Do these results extend to environments with multiple effort/quality levels?

• Effects of incomplete information/”irrational” players

• Is it possible to improve efficiency even more?

Open issues in online reputation Open issues in online reputation mechanismsmechanisms

• Feedback elicitation

– IC mechanisms for participation and truth-telling exist if raters independent

– However, they are all vulnerable to collusion

• Accounting for bounded rationality

• Comparative institutions

– Under what conditions reputation outperforms litigation

efficiency and robustness of binary online feedback...

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