Pseudonyms in Cost-Sharing Games Paolo Penna Florian Schoppmann Riccardo Silvestri Peter Widmayer Università di Salerno Stanford University Università di RomaETH Zurich

Cost-Sharing Games S 1.Which users to service? 2.At which price? Users Service Users willingness to pay

Cost(s) = Cost-Sharing Games Users Service a bc S Cheat! Users willingness to pay /3 2/3 2/3 1/2 1/2 1 Identical prices

Cost-Sharing Games S Users Service Group Strategyproof (GSP): no cheating, even for coalitions Depends on S!! none worse, one better Voluntary Participation, Consumer Sovereinity minimal requirements Budget Balance (BB) : sum payments = total cost

Mechanisms Mechanisms are (essentially) methods to divide the cost –[Moulin 99, Moulin&Shenker01, Immorlica&Mahdian&Mirrokni05] Different prices do help –[Bleischwitz&Monien&Schoppmann&Tiemann 07] GSP + BB

Different prices b cd a bc /2 1/2 1/2 1/ /2 1/2 Change name! Internet: no identity verificationVirtual identities, pseudonyms GSP + BB [Bleischwitz et al 07] 1/2

This work a,d b c BB + GSP + Renameproof 1.Symmetric games 2.Deterministic 3.No multiple bids u(a)u(d) Renameproof: no incentive to change your current name (no better utility) = Names a c d b no incentive to change name Are there mechanisms that “resist to pseudonyms”? not GSP a bc random

Main Results BB + GSP + Renameproof General impossible! Concave only one mechanism  Identical prices

Main Results BB + GSP + Renameproof  Identical prices approximate new mechanisms ?! relax Reputationproof use reputation to rank users reputation helps!

BB + GSP + Renameproof  Identical prices S Names S a da d Price does not depend on “a” Price(S) Price(S  {a}, a)Price(S  {d}, d)

S BB + GSP + Renameproof  Identical prices S Names S a da d Price(S) 3 users:

BB + GSP + Renameproof  Identical prices S Names S a da d 3 users: x1x1 x3x3 x2x2 x1 +x2 + x3 = 1 Cost(3) For all triangles!!

BB + GSP + Renameproof  Identical prices S Names S a da d 3 users: Color edges of complete graph on n nodes s.t. every triangle has weight 1 x1 +x2 + x3 = 14 names: d 1/2 1/4 ab c 1/2

BB + GSP + Renameproof  Identical prices S Names S a da d 3 users: x1 +x2 + x3 = 1 Color edges of complete graph on n nodes s.t. every triangle has weight 1 Only this!! 1/3

BB + GSP + Renameproof  Identical prices S Names S a da d s+1 users: x1 +x2 + x3+x4 = 1 Color the complete hypergraph on n nodes s.t. every (s+1)-subset sums up to 1

BB + GSP + Renameproof  Identical prices apx-“approx” LB( , s)  x(S)  UB( , s) 1/(s+1) s+1 users: Color the complete hypergraph on n nodes s.t. every (s+1)-subset sums up to 1 x1x1 x3x3 x2x2 1  x1 +x2 + x3   For all triangles!! q  [1,  ] S U V same same color

BB + GSP + Renameproof  Identical prices apx-“approx” LB( , s)  x(S)  UB( , s) s+1 users: Color the complete hypergraph on n nodes s.t. every (s+1)-subset sums up to 1 q  [1,  ] Prices are always bounded… |x(S) – x(S’)|   …sometimes “identical” Monocromatic Ramsey Theorem Service

Main Results BB + GSP + Renameproof  Identical prices relax Reputationproof use reputation to rank users reputation helps!

Renameproof R Names R a da d 5 years ago 2min ago timenewcomer

Renameproof R Names R a da d Seller: paolo.penna Feedback: 107 Positive Seller: ppenna Feedback: 1 Positive reputation

Renameproof aNamesa”a’ aReputationa”a’ Not possible worse reputation  no better price Reputationproof

2/3 1/3 1 alow reputation a”a’ GSP + BB high reputation 7 5 1/ /2

Reputationproof alow reputation a”a’ GSP + BB high reputation 1 1/2 1/2 1/2 1/2 1

Conclusions Renameproof mechanisms identical prices randomization concave not obvious new mechanisms? Reputationproof mechanisms better reputation  better price Social Cost of Cheap Pseudonyms [Friedman&Resnik 01] Sybil Attacks [Douceur 01, Cheng&Friedman 05] Falsenameproof [Yokoo&Sakurai&Matsubara 04] newcomers vote many timesbid many times

Conclusions Renameproof mechanisms identical prices randomization Social Cost of Cheap Pseudonyms [Friedman&Resnik 01] Sybil Attacks [Douceur 01, Cheng&Friedman 05] Falsenameproof [Yokoo&Sakurai&Matsubara 04] bid many times 1/3 1/3 1/3 1/2 1/2 1 Public excludable good 1/3 11

Thank You

Randomization? a bc 2-  2-  2-   1/3 a bc  2/3 GSP [BMST07] not GSP