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) “ Towards a Science of Networks” Workshop Sounion, Greece – September 1, 2006 Work partly funded by EuroNGI Network of Excellence (IST )

2 Overview Problem definition and related work The basic model and its analysis fixed punishments The extended model and its analysis reputation-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 lying Punishment 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 [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 act both 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 participants N is either fixed or mean number of participants with geometrically distributed lifetimes Time is partitioned in rounds During 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 latter A provider i is selected during a round with probability proportional to his rank Each participant has a probability a i to provide a service instance successfully, with satisfactory quality a i is private information, estimated by reputation –e.g. percentage of past successful provisions

11 Costs, Payments, Ratings A successfully provided service instance: Offers fixed utility u to the client Demands 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 provided Upon agreement, the client pays (1-p)·b and the vote is registered for updating the provider’s reputation Upon disagreement a fixed punishment c is imposed to both

12 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 participants A positive rating results in payoff impact w p > 0 for the provider and -w c < 0 for the client A negative rating results in payoff impact -w p 0 for the client Payoff impacts are taken independent of current reputation ~ ~

u-b-w c b-v+w p 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+w c ’ p·b-v-w p ’ 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+w c ’ p·b-w p ’ -p·b-c p·b-c -p·b-c p·b-c -p·b-c p·b-c -p·b-w c p·b+w p -p·b-c p·b-c -p·b-c p·b-c -p·b-c p·b-c -p·b p·b client provider success failure aiai 1-a i Witness Lie Duck Witness Lie Duck ~ ~ ~ ~

14 Truthful-Rating Equilibrium under the Basic Model

15 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 cases Success: provider  Witness and client  Lie or Duck Failure: client  Witness and provider  Lie or Duck Witness is best response to itself when c > (1-p)·b+w c and c > w p Does this equilibrium indeed arise ? Is it stable ? ~

16 Evolutionary Stability Evolutionary Stable Strategy (ESS): 1. Nash equilibrium 2. 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 π s played by a population fraction x s :

17 Stable Truthful Rating (x 1, x 2, x 3 ) are the population fractions of providers that play Witness, Lie, Duck in the success sub-game (y 1, y 2, y 3 ) are these fractions for clients Basin of attraction of truthful-rating equilibrium:  Region for population mix that ultimately leads all participants to play Witness  (x 1, x 2, x 3 ) = (1,0,0) and (y 1, y 2, y 3 ) = (1,0,0)

18 The Basin of Attraction of Truthful Rating Success sub-game X  Y

19 The Basin of Attraction of Truthful Rating Failure sub-game X’  Y ’

20 The Extended Model

21 Differences from Basic Model Disagreement punishment is not fixed Depends on the transacted participant’s: –Rank, i.e. reputation –Role which are public information Payoff impacts of a vote w p, -w c, w p, -w c are not taken fixed Calculated explicitly ~~

22 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 incentives Now, rank impacts are not time-dependent; e.g.

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.

24 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 ranksuccess probability mean success probability  payoff as client  payoff as provider

25 The Conditions on Punishments Provider’s punishment: Client’s punishment: Since N is large, f p is approximated by a simple formula This is bounded from above and below

26 Numerical Example N=50, q=0.4, p=0.2, b=2, u=2.5, v=0.5,  =0.6,  =0.9 R Disagreement Payoff Impact w p (R), w c (R) Provider Client Punishment for Disagreement R ~

27 Social Benefit Estimation

28 Social Loss Disagreement punishment is unfairly induced to one of the transacted participants  social loss When punishment is fixed, c > q w p + (1-q)[(1-p)b+w c ] The maximum payoff impacts w p, w c have to be assumed Thus, unfairness is induced for all the non-highest ranked participants  greater social loss Reputation-based punishments eliminate this unfairness! ~ ~

29 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 Reputation-based Punishment Fixed Punishment

30 Concluding Remarks

31 Summary of our Contribution Proposed a simple mechanism that provides incentives for truthful rating in an interesting context of an e-marketplace Reputation-based competition Dual role of participants Derived conditions on the effectiveness of such a mechanism with fixed punishments Stability analysis of truthful-rating Nash equilibrium Derived tailored reputation-based punishments Significant 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