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

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)

=

[email protected]

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