Enforcing Truthful-Rating Equilibria in Electronic Marketplaces

1. 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 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 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 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 ai to provide a service instance successfully, with satisfactory quality • ai 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 punishmentc 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 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 ~ ~

13. client Witness Lie Duck provider Witness ~ Lie ~ success Duck ai ~ Witness 1-ai ~ failure Lie Duck

14. Truthful-Rating Equilibriumunder 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+wcand c > wp • Does this equilibrium indeed arise ? • Is it stable ? ~

16. Evolutionary Stability • Evolutionary Stable Strategy (ESS): • Nash equilibrium • 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 πsplayed by a population fraction xs:

17. 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)

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 wp , -wc , wp , -wc 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 mean success probability rank success probability  payoff as provider  payoff as client

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

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

27. Social Benefit Estimation

28. Social Loss • Disagreement punishment is unfairly induced to oneof the transacted participants  social loss • When punishment is fixed, c > qwp + (1-q)[(1-p)b+wc] • The maximum payoff impacts wp , wchave 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 • Social benefit: Ratio of average reputation-based punishment over fixed punishment • for various mean-reputation values of the population Reputation-basedPunishment Fixed Punishment Population’s mean-reputation • Normal distribution of ranks with (μ, σ)=(1, 0.5)

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