CRESCCO Project
IST-2001-33135
Work Package 2
Critical Resources and
Selfish Agents
Paolo Penna
Università di Salerno
M.I.T. (majana institute of technology )
[email protected]
Project funded by the Future and Emerging Technologies arm of
the IST Programme – FET Proactive initiative “Global
Computing”
SELFISH
DIFFERENT
DIFFERENT
ENTITIES
SOCIO-ECONOMIC
GOALS
THAT COOPERATE
ENTITIES
AUTONOMOUS
SYSTEMS
PROVIDERS
INTERNET
INTERNET
PRIVATE
COMPANIES
UNIVERSITIES
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 Goals
1. A deeper understanding of basic principles
of a complex system (Internet)
Strict and centralized vs loose and local control
What is the price of anarchy?
2. Methodology to develop good solutions
Design a new “TCP/IP protocol” robust wrt selfish users
3. New concepts, mathematical tools and
algorithmic techniques
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 Progress
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.
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.
APPLICATIONS (workpackages): WIRELESS
SCHEDULING/ROUTING
EXPERIMENTS
NEW GAME
NETWORKS
THEORY:
(WP5): [2,5,6,7]
[7]
(WP1):
(WP1):[5,6,7]
[1,2,3,4]
Routing/Scheduling
Scheduling Selfish Machines:
Selfish users own the links and privately know their speeds
source
s1 0
s2
0
sm 0
destination
•Unsplittable traffic J1, J2 ,…,Jn
•We look at the network congestion (makespan)
Mechanism design
Mechanism:
M=(A,P)
Computes a solution
X=A(r1,r2,…, ri ,…,rn )
Provides a payment
Pi(r1,r2,…, ri ,…,rn )
t1,t2,…, ti ,…,tn
cost
true
input
i(X,t
i)
Agents’ GOAL: maximize their own utility
ui (ri) := Pi(r1,r2,…, ri ,…,rn ) – costi(X,ti)
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
[Archer and Tardos, STOC 2001]
M=(A,P) strategyproof
Translation techniques
Algorithm
Mechanism
A
A
hard
M=(A,P)
A’
loss of performance
M=(A’,P)
Translation techniques
(selfish machines)
Not needed
A
A
“easy”
A’=A
A’
c-apx
c’-apx
A black-box, polytime
greedy (like) and
speeds si=2k
offline: c’ = c(1+)
online: c < c’  c•
[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.
Loss of performance
Online vs Offline (m=2)
online
offline
“<“ is possible
3/2  c   hardest
 c’  c•1.78
(1+)
(1+)
unselfish
selfish
[2] V. Auletta, R. De Prisco, P. Penna, and G. Persiano. On designing truthful
mechanisms for online scheduling. Proc. of SIROCCO, 2005.
“Unknown” input
Input:
jobs
future
speeds
loss
selfish
1+
selfish
  loss < 1.83
Verification

<
loss <

<
<

[Aulettaloss
et al, ICALP’04]
selfish
selfish
future
selfish
 < loss < 
[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.
Cost-Sharing Games
Service provider
S
Customers
Q
U
ti = willingness to pay
1. Which customers to service?
2. At which price?
Cost-Sharing Games
Service provider
S
Customers
Q
U
1. Budget balanced: Cost(Q) =  Pi
2. Users can form coalitions

Group strategyproof mechanisms
Cost-Sharing Games
Service provider
Customers
S
Q
U
Multicast:
S
S
1
1
0.9
0.9
wired
0.9
0.9
wireless
Cost-Sharing Games
A
[Moulin-Shenker’97]
A=OPT
A
[7]
A  any
M=(A,P)
(1+)-APX
NP-hard
M=(A,P)
OPT
(wired:polytime)  (wireless: NP-hard)
[7] P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 200
Cost-Sharing Games
A
M=(A,P)
A=OPT
A
(1+)-APX
NP-hard
[7]
M=(A,P)
Free-riders (fairness)
[5] P. Penna and C. Ventre. Free-riders in Steiner tree cost-sharing games. Proc. of SIROCCO, 2005.
[7] P. Penna and C. Ventre. More powerful and simpler cost-sharing methods. Proc. of WAOA, 200
Cost-Sharing Games
A
M=(A,P)
A=OPT
A
[7]
[6]
(1+)-APX
NP-hard
M=(A,P)
characterization
[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, 200
This year:
Recommendations
and future plans
(from 2nd year review talk)
1. Consider Algorithms and Game Theory jointly
2. Technological Issues
1. Wireless vs Wired [5,6,7]
2. Assumptions (e.g., link speeds) [1,4]
3. How much technology can help (e.g. verification,
known users traffic vs known router speeds) [2,3]
3. New concepts, new mathematical tools and new
algorithmic techniques [2,5,6,7]

Cross fertilization between TCS, micro-economics and
game theory
M.I.T. (majana institute of technology )
Answered Questions
1. 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)
3rd
Computational issues
•Efficiency, extract infos
Technological issues
•Different assumptions
Existing game theory
•Not always suitable
New Algorithms
[1-4,7,8]
[1-4]
New Game Theory
[6,3]
2nd year work: ICALP (2), IFIP-TCS, SPAA,[2,3,5-6]
STACS,
Provably
Better
Theory
SIROCCO, Technology
Theor.
Comp. Helps
Sci.
Thank You
Combining Tools ?
Theory of Computing
Efficient
(polytime apx algorithm)
Game Theory

Incentive compatible
(strategyproof mechanism)
“Good Protocol”:
part doresource
we change?
1. RunWhich
fast, optimal
allocation
2. Agents “follow” the protocol
New Game Theory: Helpful?
Verification:
1. Offline Scheduling, NO
2. Online Scheduling, YES
Cost-Sharing Methods
1. YES
Other Issues:
1. Technology
2. Fairness
M.I.T. (majana institute of technology )
New Game Theory
A
hard
loss
A
easier
A’
M=(A’,P)
new game theory
A’
no loss, provably better
M=(A’,P)
Scheduling Selfish Jobs
No selfish routing Use a scheduler
1. Users cannot refuse the allocation
2. 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:
10E
2E
1E
3E
10E
2E
11E
8E
Source
(e.g., popular sport event)
GOAL: maximize benefits-costs
[8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks.
Technical report of CRESCCO, 2003. Also submitted for publication.
Mechanism Design Theory
Problems
Consistent problems
Utilitarian problems
Most Reliable Path
Arbitrage
Task Scheduling
Knapsack
VCG
[1961]
M.I.T. (majana institute of technology )
[6] G. Melideo, P. Penna, G. Proietti, R. Wattenhofer, and P. Widmayer. Truthful mechanisms
for generalized utilitarian problems. Technical report of CRESCCO, 2003
Mechanisms for Wireless Networks
Polynomial-time mechanisms:
General
graphs
Trees,
“Metric-tree” graphs
Lower bound
No R-APX,
every R>1
Upper bound
OPT, distributed
mechanism
Distributed
Suggests a better
APX mechanism
new broadcast
for other
algorithm
cases
[7] P. Penna and C. Ventre. Energy-efficient broadcasting in ad-hoc networks: combining MSTs
with shortest-path trees. Technical report of CRESCCO, 2003.
[8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks.
Technical report of CRESCCO, 2003.
Mechanisms for Wireless Networks
Polynomial-time VCG-based mechanisms:
Lower
bound
General
graphs
Upper
bound
No R-APX,
every R>1
Metric,
remain
Well-spread NP-hard
1.5-APX
O(1)-APX
[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.
Mechanisms for Wireless Networks
• Ad Hoc Nets:
k
poweri(j)
j
i
GOAL: Strong connectivity,
Private knowledge of i
minimal total power
[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.
Nash equilibria for selfish routing
…
source
1
2
destination
Layered graphs
Identical links
l
Theorem [5]: Every l-layered network has
Corollary:
1-layered
graphs are
the worst
coordination
ratio
at l-layered
most
Theorem
[5]:
Some
networks
doinstances.
not have
pure Nash equilibria.
O(log m/log log m)
[5] S. Kontogiannis, D. Fotakis and P. Spirakis. Selfish unsplittable flows.
Technical report, Computer Technology Institute, 2003.
Bayesian-Nash
Scheduling Selfish Jobs
Speed ratio
r=smax/smin
r    1.61
1 r  2
Lower bound
r 1
1
2r 2  r
1 1

min r ,1   
2 r

Upper bound
1
m 1
r 1
r
No exact with Exact (non polytime)
(polytime)
ε
Different
job per agent,1
Bayesian-Nash
identicalspeeds,
speeds one dominant
Bayesian-Nash
strategies
r 1
M.I.T. (majana institute of technology )
[2] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. How to tax and route selfish
unsplittable traffic. Technical report of CRESCCO, 2003.
Scheduling Selfish Jobs
k vs m
k m
k m
Lower bound
k 2
k 2
m2
m3
m4
any m
7
6
4
3
Upper bound
3/ 2  ε
2
3/ 2  ε
9/ 4ε
3 ε
41  1 / m
Identical speeds, k jobs per agent, Bayesian-Nash
[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
Scheduling Selfish Machines
Machine
speeds
Our result
Any
4+ 
Previous
results
[ArcTar01]
3+
Divisible
2+
3+
Randomized, no dominant strategies
Deterministic, dominant strategies
[1] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthful
approximation mechanisms for scheduling related machines. In Proc. of STACS, 2004
Scheduling Selfish Machines
Machine
speeds
Our result
Any
4+ 
Previous
results
[ArcTar01]
3+
Divisible
2+
3+
Real cases (e.g., Sonet/SDH standards)
[1] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. Deterministic truthful
approximation mechanisms for scheduling related machines. In Proc. of STACS, 2004
Approximation and selfish agents
Applications of restricted one-parameter agents:
Selfish Jobs
1. (1+)-APX mechanism (breaks lower bounds in [2])
Selfish Machines:
1. first (1+)-APX mechanism
2. breaks a lower bound in [ArcTar01] for a weighted
variant of scheduling
Verification helps!
[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
Approximation and selfish agents
We introduce restricted one-parameter agents

No need for new algorithms!
(TCS gets its revenge)
[3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verification for
one-parameter agents. Technical report of CRESCCO, 2003.
Approximation and selfish agents
We introduce restricted one-parameter agents
Theorem [3]: Polynomial-time c-approximation
algorithm A

M = (A , P) truthful polynomial-time (c+)approximation
[3] V. Auletta, R. De Prisco, P. Penna, and P. Persiano. The benefits of verification for
one-parameter agents. Technical report of CRESCCO, 2003.
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:
10E
2E
3E
10E
2E
11E
Source
(e.g., popular sport event)
GOAL: maximize benefits-costs
[8] P. Penna and C. Ventre. Sharing the cost of multicast transmissions in wireless networks.
Technical report of CRESCCO, 2003.
Nash equilibria for selfish routing
…
1
1/m
1
1
Expected
Expected
MAX
LOAD:
MAX LOAD: 1
Θ(ln m/ln ln m)
M.I.T. (majana institute of technology )
Price of anarchy
Worst-case equilibria
Coordination ratio
Routing/Scheduling
Scheduling
Selfish Routing:
SelfishMachines:
Jobs:
Scheduling
Selfish
Selfish
users choose
usersown
own
the best
thelinks
traffic
path and
for
and
their
privately
own know
traffic
knowtheir
theirspeeds
weights
Selfish
users
the
privately
source
destination
•m links with different speeds s1, s2,…,sm
•Unsplittable traffic t1, t2 ,…, tn
•We look at the network congestion (makespan)
Routing/Scheduling
Scheduling
SchedulingSelfish
Selfish
Machines:
Jobs:
Selfish
Selfish
users
users
own
own
thethe
links
traffic
andand
privately
privately
know
know
their
their
speeds
weights
source
destination
•m links with different speeds s1, s2,…,sm
•Unsplittable traffic t1, t2 ,…, tn
•We look at the network congestion (makespan)