Pseudonyms in Cost-Sharing Games Paolo Penna Florian Schoppmann Riccardo Silvestri Peter Widmayer...
Transcript of Pseudonyms in Cost-Sharing Games Paolo Penna Florian Schoppmann Riccardo Silvestri Peter Widmayer...
Pseudonyms inCost-Sharing Games
Paolo
PennaFlorian
SchoppmannRiccardo Silvestri
Peter Widmayer
Università di Salerno Stanford University Università di Roma ETH Zurich
Cost-Sharing Games
S
1. Which users to service?2. At which price?
Users
Service
Users willingness to pay
Cost(s) =
2
s
Cost-Sharing Games
Users
Service
a b c
S Cheat!
Users willingness to pay
1 0.6 0.61
0.6-0.50
2/3 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 betterVoluntary 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 c d
0.6 0.6 1
a b c
1.1 0.6 0.6
1 1/2 1/2 1/2 1/2 1
1 1/2 1/2
Change name!
Internet: no identity verificationVirtual identities, pseudonyms
GSP + BB[Bleischwitz et al 07]
1/2 1/2
This work
a,d b c
BB + GSP + Renameproof
1. Symmetric games 2. Deterministic3. No multiple bids
u(a) u(d)
Renameproof: no incentive to changeyour current name (no better utility)
=
Names
a c
db
no incentive to change name
Are there mechanisms that “resist to pseudonyms”?not GSPa b c
random
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
Names
a dad
Price does not depend on “a”Price(S)
Price(S{a}, a) Price(S{d}, d)
BB + GSP + Renameproof Identical prices
S
Names
S
Names
a dad
3 users:
x1x3
x2
x1 +x2 + x3 = 1
Cost(3)For all triangles!!
BB + GSP + Renameproof Identical prices
S
Names
S
Names
a dad
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
1/41/4
1/2
BB + GSP + Renameproof Identical prices
S
Names
S
Names
a dad
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
1/3 1/31/3
1/31/3
1/3 1/3
1/3 1/3
BB + GSP + Renameproof Identical prices
S
Names
S
Names
a dad
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
x1x3
x2
1 x1 +x2 + x3
For all triangles!!
q [1, ]
xA1 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
Names
a dad
[email protected] [email protected]
5 years ago 2min ago
timenewcomer
Renameproof
R
Names
R
Names
a dad
Seller: paolo.pennaFeedback: 107 Positive
Seller: ppennaFeedback: 1 Positive
reputation
Renameproof
aNames a”a’
aReputation a”a’
Not possible
worse reputation no better price
Reputationproof
Conclusions
Renameproof mechanisms• identical prices• randomization
concavenot 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]
newcomersvote 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 1 1