CRESCCO ProjectIST-2001-33135

Work Package 2

Algorithms for Selfish AgentsAlgorithms for Selfish Agents

V. Auletta, P. Penna and G. PersianoV. Auletta, P. Penna and G. Persiano

Università di SalernoUniversità di Salernopino.persiano@unisa.itpino.persiano@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”

PROVIDERS

DIFFERENT SOCIO-ECONOMIC ENTITIES DIFFERENT GOALS

INTERNET

SELFISH ENTITIES THAT COOPERATE AUTONOMOUS SYSTEMS

UNIVERSITIES

INTERNET

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 protocol” robust wrt selfish users

Mathematical Tools

Theory of Computing

Microeconomics and Game Theory

Computational complexityDesign and Analysis of Algorithms

Nash equilibria

Mechanism design

Research Progress

Nash equilibria for routing problems:

Efficient mechanism design

Feasibility, optimality of the solution;

Existence, worst case, complexity

Nash equilibria

When no selfish agent has an incentive in changing his/her strategy:

(3,3) (0,5)

(5,0) (1,1)Player 1

Player 2

No other strategy improves the current payoff!

a

b

a b

Prisoner’s dilemma

Nash equilibria for routing problems

source destination

•m links with different speeds•Unsplittable traffic t1, t2 ,…, tn

•We look at the network congestion (max load)

•Selfish users choose the best path for their own traffic

Nash equilibria for routing problems

1. D. Fotakis, S. Kontogiannis, E. Koutsoupias, M. Mavronicolas, and P.Spirakis. “The Structure and Complexity of Nash Equilibria for a Selfish Routing Game.” Proc. of the Int. Colloquium on Automata, Languages and Programming (ICALP), 2002.

2. E. Koutsoupias, M. Mavronicolas and P. Spirakis, “Approximate Equilibria and Ball Fusion.” Proc. of the 9th Int. Colloquium on Structural Information and Communication Complexity, June 2002.

3. A. Ferrante and M. Parente. “Existence of Nash Equilibria in Selfish Routing problems.” Technical Report, Università di Salerno, 2002.

Nash equilibria for routing problems

…

1 1 1 Expected MAX LOAD: 1

1/nExpected MAX LOAD:

Θ(ln n/ln ln n)

…

1 2n

SUPPORT

Characterizing Nash equilibria: -- Existence for a given support set [3]

…

1 2 m

Computing Nash equilibria : -- For a given support, the best, the worst, any [1,3]Approximate Nash equilibria : -- users change strategy only if a sufficiently

better one exists [2]

Achieved Results

Characterizations of Nash equilibria:-- with a given support [3]

Computing Nash equilibria:-- the best and the worst are NP-hard [1]-- any generalized fully mixed in P [1]

-- is #P-complete [1],

Computing the cost of a Nash equilibrium:

-- but can be well approximated [1]

Mechanism design

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

•Unsplittable traffic t1, t2 ,…, tn

•We look at the network congestion (makespan)

•Selfish users owns the links and privately know their speeds

source destination

Mechanism design

Task scheduling on related machines:

• m machines of with speeds s1 s2,…,sm

• n jobs of weight t1,t2,…,tn

• Each machine is owned by a selfish agent, and agents should reveal the speed of their own machine to the system

Mechanism design

•A machine i of speed si receiving load li incurs in a cost of li/si

•We pay the agents to provide an incentive in revealing the true speed

•Agents want to maximize their utility ui := paymenti – costi

Truthful Mechanisms

Truth-telling is always the best strategy:

for any agent i and for any false declaration bi

ui(si) ≥ ui(bi)

Mechanism design

• Classical problem from microeconomics– Vickrey Clarke Groves (VCG) mechanisms

• Unsuitable for our settings– VCG only applies to utilitarian problems

• minimize sum of costs

• instead we minimize max of costs

– Requires solving optimally hard combinatorial problem

Mechanism Design

• Extensions of VCG to non-utilitarian problems– P. Penna, G. Proietti, R. Wattenhofer and P.

Widmayer. Truthful mechanisms for consistent problems. Submitted.

Mechanism design• Scheduling related machines

• Truthful mechanisms must allocate jobs monotonically: an agents declaring higher speed does not get less load;

• A monotone algorithm can be turned into a truthful mechanism with the same performances.

[Archer and Tardos 2001]

Truthful Mechanisms

Existing approximation algorithms are not monotone!!

[Archer and Tardos 2001]

We need new approximation algorithms

Research Progress

1. V. Auletta, R. De Prisco, P. Persiano, and P. Penna. “Deterministic Truthful Approximation Mechanisms for Scheduling Related Machines”. Manuscript in preparation.

Very close to a polynomial-time (2+ε)-approximation truthful mechanism.

[3-approximation mechanism truthful in expectation only, Archer et al. 01]

Research Progress

PTAS= OPT(t1,t2,…,th) + GREEDY(th+1,…,tn)

Not monotone

New monotone GREEDY algorithm

Future Plans1. A deeper understanding of basic principles in the Internet

2. Methodology to develop good solutions

3. New concepts, new mathematical tools and new algorithmic techniques

4. Cross fertilization between TCS, micro-economics and game theory

Thank You

CRESCCO ProjectIST-2001-33135

Work Package 2

Algorithms for Selfish AgentsAlgorithms for Selfish Agents

G. PersianoG. Persiano

Università di SalernoUniversità di Salernopino.persiano@unisa.itpino.persiano@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”