CRESCCO ProjectIST-2001-33135

Work Package 2

Critical Resources and Selfish Agents

Paolo PennaPaolo PennaUniversità di SalernoUniversità di Salerno

penna@dia.unisa.itpenna@dia.unisa.it

Project funded by the Future and Emerging Technologies arm of Project funded by the Future and Emerging Technologies arm of the IST Programme – FET Proactive initiative “Global the IST Programme – FET Proactive initiative “Global Computing”Computing”

M.I.T. (majana institute of technology)

DIFFERENT SOCIO-ECONOMIC ENTITIES DIFFERENT GOALS

INTERNET

SELFISH ENTITIES THAT COOPERATE

INTERNET

PROVIDERSAUTONOMOUS SYSTEMS

UNIVERSITIES

PRIVATECOMPANIES

The Internet

Open, self organized, no central authority, anarchic:

1. A router may forward packets to optimize its own traffic

2. A client may “ignore” the server ackws and not follow the TCP packet transmission rate

3. An Autonomous System may report false link status to redirect traffic to another AS

Main Goals1. A deeper understanding of basic principles of a complex system (Internet)

2. Methodology to develop good solutions

3. New concepts, mathematical tools and algorithmic techniques

Strict and centralized vs loose and local controlWhat is the price of anarchy?

Design a new “TCP/IP protocol” robust wrt selfish users

M.I.T. (majana institute of technology)

Mathematical Tools

Theory of Computing•Computational complexity•Design and Analysis of Algorithms

Microeconomics and Game Theory•Nash equilibria•Mechanism design

Research Progress1. P. Ambrosio and V. Auletta. Deterministic Monotone Algorithms

for Scheduling on Related Machines. In Proc. of WAOA, 2004.2. V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On

designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005.

3. V. Auletta, R. De Prisco, P. Penna, and G. Persiano. Monotone algorithms characterize mechanisms for selfish jobs. CRESCCO TR, 2004.

4. V. Auletta, A.V. Fishkin, and G. Persiano. On gaining a control over two links occupied by selfish agents. CRESCCO TR, 2004.

5. P. Penna and C. Ventre. Free-riders in Steiner tree cost-sharing games. Proc. of SIROCCO, 2005.

6. P. Penna and C. Ventre. When is cost-sharing possible? CRESCCO TR, 2004.

7. P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 2004.

SCHEDULING/ROUTING (WP1): [1,2,3,4]NEW GAME THEORY: [2,5,6,7]EXPERIMENTS (WP5): [7]APPLICATIONS (workpackages): WIRELESS NETWORKS (WP1): [5,6,7]

Routing/Scheduling

•Unsplittable traffic J1, J2 ,…,Jn

•We look at the network congestion (makespan)

source destination

Scheduling Selfish Machines:Selfish users own the links and privately know their speeds

s1

sm

s2

0

0

0

Mechanism design

Mechanism: M=(A,P)

Computes a solution

X=A(r1,r2,…, ri ,…,rn )

Provides a payment

Pi(r1,r2,…, ri ,…,rn )

Agents’ GOAL: maximize their own utility ui (ri) := Pi(r1,r2,…, ri ,…,rn ) – costi(X,ti)

costi(X,ti) t1,t2,…, ti ,…,tn

true input

Mechanism design

Strategyproof mechanisms:

no incentive to lie (report ri ti)

ui (ti) ui (ri)

(truth-telling is the best strategy)

Mechanism design

Question: Given A, is there P s.t.

M=(A,P)

is strategyproof?

In general, NO!

Scheduling Selfish Machines

Monotone algorithms: an agent declaring a higher speed does not get less work/load.

A monotone M=(A,P) strategyproof

[Archer and Tardos, STOC 2001]

Translation techniques

A’A M=(A’,P)

Algorithm Mechanism

M=(A,P)A

hard

loss of performance

Translation techniques

A black-box, polytime

A’A“easy”

c-apx c’-apxoffline: c’ = c(1+)online: c < c’ c•

A’=AA

Not needed

[1] P. Ambrosio and V. Auletta. Deterministic Monotone Algorithms for Scheduling on Related Machines. In Proc. of WAOA, 2004.[2] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005.

greedy (like) andspeeds si=2k

(selfish machines)

Loss of performance

[2] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005.

Online vs Offline (m=2)

offline

online

selfishunselfish

(1+) (1+)

3/2 c c’ c•1.78

“<“ is possible

hardest

“Unknown” input

[2] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful mechanisms for online scheduling. Proc. of SIROCCO, 2005.

Input: jobs speeds loss

1+

[3] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. Monotone algorithms characterize mechanisms for selfish jobs. CRESCCO TR, 2004.

selfish

loss < 1.83selfishfuture

< loss <

selfish

selfish future selfish

< loss < < loss < Verification[Auletta et al, ICALP’04]

Cost-Sharing Games

UQ

1. Which customers to service?2. At which price?

S

Service provider Customers

ti = willingness to pay

Cost-Sharing Games

UQS

Service provider Customers

1. Budget balanced: Cost(Q) = Pi

2. Users can form coalitions Group strategyproof mechanisms

Cost-Sharing Games

UQS

Service provider Customers

S

0.9 0.9

1

Multicast:S

0.9 0.9

1

wired wireless

Cost-Sharing Games

M=(A,P)[Moulin-Shenker’97]

A

A=OPT (1+)-APXNP-hard

A any OPT (wired:polytime)

M=(A,P)[7]

A

[7] P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 2004.

(wireless: NP-hard)

Cost-Sharing Games

M=(A,P)A

A=OPT (1+)-APXNP-hard

Free-riders (fairness)

[5] P. Penna and C. Ventre. Free-riders in Steiner tree cost-sharing games. Proc. of SIROCCO, 2005.

M=(A,P)[7]

A

[7] P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 2004.

Cost-Sharing Games

M=(A,P)A

A=OPT (1+)-APXNP-hard

[5] P. Penna and C. Ventre. Free-riders in Steiner tree cost-sharing games. Proc. of SIROCCO, 2005.

M=(A,P)[7]

A

[7] P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 2004.

[6] P. Penna and C. Ventre. When is cost-sharing possible? CRESCCO TR, 2004.

[6] characterization

Recommendations and future plans (from 2nd year review talk)

1. Consider Algorithms and Game Theory jointly2. Technological Issues

1. Wireless vs Wired2. Assumptions (e.g., link speeds)3. How much technology can help (e.g. verification,

known users traffic vs known router speeds)3. New concepts, new mathematical tools and new

algorithmic techniques

Cross fertilization between TCS, micro-economics and game theory

[5,6,7][1,4]

[2,3]

[2,5,6,7]

M.I.T. (majana institute of technology)

This year:

Answered Questions1. When verification helps:

Online YES, offline NO [2]2. Online Setting:

More difficult! [2]3. Selfish Jobs vs Selfish Machines:

Constant loss [3]4. Wireless Networks:

Budget-balance, Wireless vs Wired [6,7]5. Mechanism Design Theory:

Problem restrictions [6,7]

Important Issues (2nd year review talk)

Computational issues•Efficiency

Technological issues•Different assumptions

Existing game theory•Not always suitable

New Algorithms[1-4,7,8]

New Game Theory[6,3]

, extract infos

Provably Better2nd year work: ICALP (2), IFIP-TCS, SPAA, STACS, SIROCCO, Theor. Comp. Sci.

[1-4]

[2,3,5-6]

3rd

Technology Helps Theory

Thank You

Theory of Computing Game Theory

Combining Tools

Efficient Incentive compatible(strategyproof mechanism)(polytime apx

algorithm)

Which part do we change? “Good Protocol”:1. Run fast, optimal resource allocation2. Agents “follow” the protocol

?

New Game Theory: Helpful? Verification:

1. Offline Scheduling, NO2. Online Scheduling, YES

Cost-Sharing Methods1. YES

Other Issues:1. Technology2. Fairness

M.I.T. (majana institute of technology)

New Game Theory

A’A M=(A’,P)

loss

hard

game theorynew

A’A M=(A’,P)easier

no loss, provably better

Scheduling Selfish Jobs

No selfish routing Use a scheduler1. Users cannot refuse the allocation2. May lie about their traffic weights

Provide correct incentives (mechanism design)

[2] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfish unsplittable traffic. Technical report of CRESCCO, 2003.

Mechanisms for Wireless Networks

• Wireless Cost-Sharing:

Source(e.g., popular sport event)

[8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks. Technical report of CRESCCO, 2003. Also submitted for publication.

10E

3E

2E 11E2E10E

GOAL: maximize benefits-costs

8E1E

Mechanism Design Theory

[6] G. Melideo, P. Penna, G. Proietti, R. Wattenhofer, and P. Widmayer. Truthful mechanisms for generalized utilitarian problems. Technical report of CRESCCO, 2003

Utilitarian problems

Consistent problems

VCG [1961]

Problems Most Reliable PathArbitrageTask SchedulingKnapsack

M.I.T. (majana institute of technology)

Mechanisms for Wireless Networks

[8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks. Technical report of CRESCCO, 2003.

Polynomial-time mechanisms: Lower bound Upper bound

General

graphs

No R-APX,

every R>1

Trees,

“Metric-tree” graphs

OPT, distributed

mechanism

Distributed APX mechanism for other casesSuggests a better new broadcast algorithm[7] P. Penna and C. Ventre. Energy-efficient broadcasting in ad-hoc networks: combining MSTs with shortest-path trees. Technical report of CRESCCO, 2003.

Mechanisms for Wireless Networks

Polynomial-time VCG-based mechanisms:

[1] C. Ambuehl, A. Clementi, P. Penna, G. Rossi, and R. Silvestri. Energy Consumption in Radio Networks: Selfish Agents and Rewarding Mechanisms. In Proc. of SIROCCO, 2003. Also accepted in Theoretical Computer Science.

Lower bound

Upper bound

General

graphs

No R-APX,

every R>1

Metric,

Well-spread

remain

NP-hard

1.5-APX

O(1)-APX

Mechanisms for Wireless Networks

• Ad Hoc Nets:

i

poweri(j) j

Private knowledge of i

[1] C. Ambuehl, A. Clementi, P. Penna, G. Rossi, and R. Silvestri. Energy Consumption in Radio Networks: Selfish Agents and Rewarding Mechanisms. In Proc. of SIROCCO, 2003. Also accepted in Theoretical Computer Science.

GOAL: Strong connectivity, minimal total power

k

Nash equilibria for selfish routing

[5] S. Kontogiannis, D. Fotakis and P. Spirakis. Selfish unsplittable flows. Technical report, Computer Technology Institute, 2003.

Theorem [5]: Every l-layered network has coordination ratio at most

O(log m/log log m)

1

…

2 l

Layered graphsIdentical links

source destination

Corollary: 1-layered graphs are the worst instances.Theorem [5]: Some l-layered networks do not have pure Nash equilibria.

Scheduling Selfish Jobs

[2] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfish unsplittable traffic. Technical report of CRESCCO, 2003.

Speed ratio

r=smax/smin

Lower bound Upper bound

identical speeds

No exact with dominant strategies

Exact (non polytime)

(polytime)

Bayesian-Nash

rr

r

22

1161.1r

1

11

r

m

1r

rr

1

2

11,min r21 r

ε1Different speeds, one job per agent, Bayesian-NashM.I.T. (majana institute of technology)

Bayesian-Nash

Scheduling Selfish Jobs

[2] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfish unsplittable traffic. Technical report of CRESCCO, 2003. Also submitted for publication

k vs m Lower bound Upper bound

6

7mk

2k

2k

ε2/3

2

3

4mk

Identical speeds, k jobs per agent, Bayesian-Nash

m/114 many

ε2/3 2m3m4m

ε4/9 ε3

Scheduling Selfish Machines

[1] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthful approximation mechanisms for scheduling related machines. In Proc. of STACS, 2004

Machine speeds

Our result Previous results [ArcTar01]

Any 4+ 3+

Divisible 2 + 3+

Randomized, no dominant strategies

Deterministic, dominant strategies

Scheduling Selfish Machines

[1] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthful approximation mechanisms for scheduling related machines. In Proc. of STACS, 2004

Machine speeds

Our result Previous results [ArcTar01]

Any 4+ 3+

Divisible 2 + 3+

Real cases (e.g., Sonet/SDH standards)

Applications of restricted one-parameter agents:Selfish Jobs

1. (1+)-APX mechanism (breaks lower bounds in [2])

Selfish Machines: 1. first (1+)-APX mechanism2. breaks a lower bound in [ArcTar01] for a weighted

variant of scheduling

Approximation and selfish agents

[3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verification for one-parameter agents. Technical report of CRESCCO, 2003. Also submitted for publication

Verification helps!

Approximation and selfish agents

[3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verification for one-parameter agents. Technical report of CRESCCO, 2003.

No need for new algorithms!

(TCS gets its revenge)

We introduce restricted one-parameter agents

Approximation and selfish agents

[3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verification for one-parameter agents. Technical report of CRESCCO, 2003.

We introduce restricted one-parameter agents

Theorem [3]: Polynomial-time c-approximation algorithm A

M = (A , P) truthful polynomial-time (c+)-approximation

Mechanism design

Mechanism: M=(A,P)

Computes a solution

X=A(r1,r2,…, ri ,…,rn )

Provides a payment

Pi(r1,r2,…, ri ,…,rn )

costi(X,ti)

Agents’ GOAL: maximize their own utility ui (r1,r2,…, ri ,…,rn ) := Pi(r1,r2,…, ri ,…,rn ) – costi(X,ti)

Mechanism design Strategyproof mechanisms: no incentive to lie

1. Bayesian-Nash

ui (t1,t2,…, ti ,…,tn ) ui (t1,t2,…, ri ,…,tn )

(truth-telling is Nash equilibrium)

2. With dominant strategies

ui (r1,r2,…, ti ,…,rn ) ui (r1,r2,…, ri ,…,rn )

(truth-telling is always the best strategy)

Mechanisms for Wireless Networks

• Wireless Cost-Sharing:

Source(e.g., popular sport event)

[8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks. Technical report of CRESCCO, 2003.

10E

3E

2E 11E2E10E

GOAL: maximize benefits-costs

Nash equilibria for selfish routing

…

1 1 1 Expected MAX LOAD: 1

1/mExpected MAX LOAD:

Θ(ln m/ln ln m) Price of anarchyWorst-case equilibriaCoordination ratio

M.I.T. (majana institute of technology)

Routing/Scheduling

•m links with different speeds s1, s2,…,sm

•Unsplittable traffic t1, t2 ,…, tn

•We look at the network congestion (makespan)

source destination

Selfish Routing:users choose the best path for their own traffic

Scheduling Selfish Jobs: Selfish users own the traffic and privately know their weightsScheduling Selfish Machines:Selfish users own the links and privately know their speeds

Routing/Scheduling

•m links with different speeds s1, s2,…,sm

•Unsplittable traffic t1, t2 ,…, tn

•We look at the network congestion (makespan)

source destination

Scheduling Selfish Jobs: Selfish users own the traffic and privately know their weights

Scheduling Selfish Machines:Selfish users own the links and privately know their speeds