Département Réseau, Sécurité et Multimédia Rapport d'Activités 2008

monopoly set prices. The performancemeasure we consider is social welfare, i.e. thetotal value that the system has for allparticipants. Under some assumptions on thepeers utility functions, we derive a necessaryand sufficient condition for symmetry-basedsystems to outperform revenue-orientedmanagement.The figure below compares social welfare Wobtained by using each scheme to the maximalreachable value of social welfare W*(assuming user preferences are parameterisedby two independent values, a and b, with anexponential distribution of respective mean1/µ a and 1/µ b ).for a type of management to be preferable tothe other: it appears that profit orientedpayment-based schemes may be socially betterthan symmetric ones under some specificcircumstances, namely if the heterogeneityamong user profiles is high.References[1] D. Fudenberg and J. Tirole. Game theory.MIT Press, 1991[2] L. Toka and P. Maillé. Managing a Peer-to-Peer Backup System: Does Imposed FairnessSocially Outperform a Revenue-DrivenMonopoly?, in Proc. of the 4th InternationalWorkshop on Grid Economics and BusinessModels (Gecon’2007, Rennes, France), August2007.[3] P. Maillé and L. Toka. Managing a Peer-to-Peer Storage System in a Selfish Society.Submitted.We obtain that user heterogeneity tends tofavor pricing-based schemes that are moreflexible, and above a given user heterogeneitythreshold even a monopoly-managed systemwill be socially better than a system imposingsymmetry. Those results have been presentedin [2], and a generalized version of the modelhas been submitted.ConclusionsIn this work we have addressed the problem ofuser incentives in a peer-to-peer storagesystem. Using a game theoretical model todescribe selfish reactions of all systems actors(users and the operator), we have studied andcompared the outcomes of two possiblemanaging schemes, namely symmetry-basedand profit oriented payment-based. Not onlythe size of the offered storage space wastargeted with incentives, but as the availabilityand reliability is a particularly important issuein storage systems, the model also aimed toreduce churn. By comparing the social welfarelevel at the outcome in the two cases, undersome assumptions on user preferences weexhibited a necessary and sufficient conditionPracom’s Annual Report 2008 61