pseudonyms in cost-sharing games paolo penna florian schoppmann riccardo silvestri peter widmayer...
TRANSCRIPT
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
Generalimpossible!
Concaveonly 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
Names
a dad
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
Names
a dad
Price(S)
3 users:
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
Reputationproof
2/3 1/3 1
alow reputation
a”a’
GSP + BB
high
reputation
75
1/2 1
50
1 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
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
Thank You
Randomization?
1 1 2 1 2 1
a b c
2- 2- 2-
1/3
a b c
3 3 3
2/3
GSP [BMST07]
not GSP